Metadata stop to be written after random period of time. Commit failed, will try again next cycle.

### Apache Iceberg version

1.9.1

### Query engine

Athena

### Please describe the bug 🐞

We are using AWS MSK Iceberg Connector.
We use plugin (zip) made of JARs built from Iceberg and aws-glue-schema-registry
ICEBERG_VERSION 1.9.1
AWS_SDK Version 2.31.78
java-17-amazon-corretto-jdk

https://github.com/awslabs/aws-glue-schema-registry/
https://github.com/apache/iceberg/

Connector runs fine, writes data, which can be queried with Athena
but after random period of time (hours, days) it fails to commit to the table.
And stucks in a cycle "Commit failed, will try again next cycle"

Then sometimes after few hours it somehow manages to commit once but then ends up stucked again.
What is interesting, that data parquet files are written to S3 but not metadata.

Attaching trace.

` java.lang.IllegalStateException: Connection pool shut down
at org.apache.http.util.Asserts.check(Asserts.java:34)
at org.apache.http.impl.conn.PoolingHttpClientConnectionManager.requestConnection(PoolingHttpClientConnectionManager.java:269)
at software.amazon.awssdk.http.apache.internal.conn.ClientConnectionManagerFactory$DelegatingHttpClientConnectionManager.requestConnection(ClientConnectionManagerFactory.java:75)
at software.amazon.awssdk.http.apache.internal.conn.ClientConnectionManagerFactory$InstrumentedHttpClientConnectionManager.requestConnection(ClientConnectionManagerFactory.java:57)
at org.apache.http.impl.execchain.MainClientExec.execute(MainClientExec.java:176)
at org.apache.http.impl.execchain.ProtocolExec.execute(ProtocolExec.java:186)
at org.apache.http.impl.client.InternalHttpClient.doExecute(InternalHttpClient.java:185)
at org.apache.http.impl.client.CloseableHttpClient.execute(CloseableHttpClient.java:83)
at org.apache.http.impl.client.CloseableHttpClient.execute(CloseableHttpClient.java:56)
at software.amazon.awssdk.http.apache.internal.impl.ApacheSdkHttpClient.execute(ApacheSdkHttpClient.java:72)
at software.amazon.awssdk.http.apache.ApacheHttpClient.execute(ApacheHttpClient.java:254)
at software.amazon.awssdk.http.apache.ApacheHttpClient.access$500(ApacheHttpClient.java:104)
at software.amazon.awssdk.http.apache.ApacheHttpClient$1.call(ApacheHttpClient.java:231)
at software.amazon.awssdk.http.apache.ApacheHttpClient$1.call(ApacheHttpClient.java:228)
at software.amazon.awssdk.core.internal.util.MetricUtils.measureDurationUnsafe(MetricUtils.java:102)
at software.amazon.awssdk.core.internal.http.pipeline.stages.MakeHttpRequestStage.executeHttpRequest(MakeHttpRequestStage.java:79)
at software.amazon.awssdk.core.internal.http.pipeline.stages.MakeHttpRequestStage.execute(MakeHttpRequestStage.java:57)
at software.amazon.awssdk.core.internal.http.pipeline.stages.MakeHttpRequestStage.execute(MakeHttpRequestStage.java:40)
at software.amazon.awssdk.core.internal.http.pipeline.RequestPipelineBuilder$ComposingRequestPipelineStage.execute(RequestPipelineBuilder.java:206)
at software.amazon.awssdk.core.internal.http.pipeline.RequestPipelineBuilder$ComposingRequestPipelineStage.execute(RequestPipelineBuilder.java:206)
at software.amazon.awssdk.core.internal.http.pipeline.RequestPipelineBuilder$ComposingRequestPipelineStage.execute(RequestPipelineBuilder.java:206)
at software.amazon.awssdk.core.internal.http.pipeline.RequestPipelineBuilder$ComposingRequestPipelineStage.execute(RequestPipelineBuilder.java:206)
at software.amazon.awssdk.core.internal.http.pipeline.stages.ApiCallAttemptTimeoutTrackingStage.execute(ApiCallAttemptTimeoutTrackingStage.java:74)
at software.amazon.awssdk.core.internal.http.pipeline.stages.ApiCallAttemptTimeoutTrackingStage.execute(ApiCallAttemptTimeoutTrackingStage.java:43)
at software.amazon.awssdk.core.internal.http.pipeline.stages.TimeoutExceptionHandlingStage.execute(TimeoutExceptionHandlingStage.java:79)
at software.amazon.awssdk.core.internal.http.pipeline.stages.TimeoutExceptionHandlingStage.execute(TimeoutExceptionHandlingStage.java:41)
at software.amazon.awssdk.core.internal.http.pipeline.stages.ApiCallAttemptMetricCollectionStage.execute(ApiCallAttemptMetricCollectionStage.java:55)
at software.amazon.awssdk.core.internal.http.pipeline.stages.ApiCallAttemptMetricCollectionStage.execute(ApiCallAttemptMetricCollectionStage.java:39)
at software.amazon.awssdk.core.internal.http.pipeline.stages.RetryableStage2.executeRequest(RetryableStage2.java:93)
at software.amazon.awssdk.core.internal.http.pipeline.stages.RetryableStage2.execute(RetryableStage2.java:56)
at software.amazon.awssdk.core.internal.http.pipeline.stages.RetryableStage2.execute(RetryableStage2.java:36)
at software.amazon.awssdk.core.internal.http.pipeline.RequestPipelineBuilder$ComposingRequestPipelineStage.execute(RequestPipelineBuilder.java:206)
at software.amazon.awssdk.core.internal.http.StreamManagingStage.execute(StreamManagingStage.java:53)
at software.amazon.awssdk.core.internal.http.StreamManagingStage.execute(StreamManagingStage.java:35)
at software.amazon.awssdk.core.internal.http.pipeline.stages.ApiCallTimeoutTrackingStage.executeWithTimer(ApiCallTimeoutTrackingStage.java:82)
at software.amazon.awssdk.core.internal.http.pipeline.stages.ApiCallTimeoutTrackingStage.execute(ApiCallTimeoutTrackingStage.java:62)
at software.amazon.awssdk.core.internal.http.pipeline.stages.ApiCallTimeoutTrackingStage.execute(ApiCallTimeoutTrackingStage.java:43)
at software.amazon.awssdk.core.internal.http.pipeline.stages.ApiCallMetricCollectionStage.execute(ApiCallMetricCollectionStage.java:50)
at software.amazon.awssdk.core.internal.http.pipeline.stages.ApiCallMetricCollectionStage.execute(ApiCallMetricCollectionStage.java:32)
at software.amazon.awssdk.core.internal.http.pipeline.RequestPipelineBuilder$ComposingRequestPipelineStage.execute(RequestPipelineBuilder.java:206)
at software.amazon.awssdk.core.internal.http.pipeline.RequestPipelineBuilder$ComposingRequestPipelineStage.execute(RequestPipelineBuilder.java:206)
at software.amazon.awssdk.core.internal.http.pipeline.stages.ExecutionFailureExceptionReportingStage.execute(ExecutionFailureExceptionReportingStage.java:37)
at software.amazon.awssdk.core.internal.http.pipeline.stages.ExecutionFailureExceptionReportingStage.execute(ExecutionFailureExceptionReportingStage.java:26)
at software.amazon.awssdk.core.internal.http.AmazonSyncHttpClient$RequestExecutionBuilderImpl.execute(AmazonSyncHttpClient.java:210)
at software.amazon.awssdk.core.internal.handler.BaseSyncClientHandler.invoke(BaseSyncClientHandler.java:103)
at software.amazon.awssdk.core.internal.handler.BaseSyncClientHandler.doExecute(BaseSyncClientHandler.java:173)
at software.amazon.awssdk.core.internal.handler.BaseSyncClientHandler.lambda$execute$1(BaseSyncClientHandler.java:80)
at software.amazon.awssdk.core.internal.handler.BaseSyncClientHandler.measureApiCallSuccess(BaseSyncClientHandler.java:182)
at software.amazon.awssdk.core.internal.handler.BaseSyncClientHandler.execute(BaseSyncClientHandler.java:74)
at software.amazon.awssdk.core.client.handler.SdkSyncClientHandler.execute(SdkSyncClientHandler.java:45)
at software.amazon.awssdk.awscore.client.handler.AwsSyncClientHandler.execute(AwsSyncClientHandler.java:53)
at software.amazon.awssdk.services.glue.DefaultGlueClient.getTable(DefaultGlueClient.java:10007)
at org.apache.iceberg.aws.glue.GlueTableOperations.getGlueTable(GlueTableOperations.java:279)
at org.apache.iceberg.aws.glue.GlueTableOperations.doRefresh(GlueTableOperations.java:128)
at org.apache.iceberg.BaseMetastoreTableOperations.refresh(BaseMetastoreTableOperations.java:88)
at org.apache.iceberg.BaseMetastoreTableOperations.current(BaseMetastoreTableOperations.java:71)
at org.apache.iceberg.BaseMetastoreCatalog.loadTable(BaseMetastoreCatalog.java:49)
at org.apache.iceberg.connect.channel.Coordinator.commitToTable(Coordinator.java:188)
at org.apache.iceberg.connect.channel.Coordinator.lambda$doCommit$1(Coordinator.java:152)
at org.apache.iceberg.util.Tasks$Builder.runTaskWithRetry(Tasks.java:413)
at org.apache.iceberg.util.Tasks$Builder$1.run(Tasks.java:315)
at java.base/java.util.concurrent.Executors$RunnableAdapter.call(Executors.java:539)
at java.base/java.util.concurrent.FutureTask.run(FutureTask.java:264)
at java.base/java.util.concurrent.ThreadPoolExecutor.runWorker(ThreadPoolExecutor.java:1136)
at java.base/java.util.concurrent.ThreadPoolExecutor$Worker.run(ThreadPoolExecutor.java:635)
at java.base/java.lang.Thread.run(Thread.java:840)`

### Willingness to contribute

- [ ] I can contribute a fix for this bug independently
- [ ] I would be willing to contribute a fix for this bug with guidance from the Iceberg community
- [x] I cannot contribute a fix for this bug at this time

Start by tracing Coordinator.commitToTable and GlueTableOperations.getGlueTable in the stack trace, then inspect how the AWS SDK Apache HTTP client is managed during repeated commits. Reproduce the connector's long-running failure and identify why the connection pool is shut down; done means commits continue successfully and the failure has a regression test.

Written by the indexing model from the issue text.