[Self-Managed]: Fleet Server doesn't gets back healthy itself when setup VM is turned off then re-run after sometime.

**Kibana Build details:**
```
VERSION: 8.11.0 SNAPSHOT self-managed
BUILD: 67254
COMMIT: 7ac96504f11ebde1f14d7cd9d45d99ed0d81768f
```

**Host OS:** Windows

**Preconditions:**
1. 8.11.0 SNAPSHOT Kibana self-managed environment should be available.

**Steps to reproduce:**
1. Setup 8.11 self-managed elasticsearch and kibana.
2. Install Fleet Server.
3. Shut down elasticsearch and kibana services. Now shut down the VM
5. Turn VM on after 10 minutes and also re-run elasticsearch and kibana again.
6. Navigate to Fleet tab and observe Fleet server keeps sending data and logs, however remain offline on UI.
[We have waited more than an hour to get the fleet server back Healthy.]
7. Agent diagnostics also fails.
8. Now run `.\elastic-agent.exe diagnostics collect`.
9. Observe agent gets back Healthy.

**Note:**
- We have observed this issue on earlier kibana versions too.
- Issue is consistent and reproducible everytime.

**Agent logs:**
[elastic-agent-diagnostics-2023-09-25T10-35-16Z-00.zip](https://github.com/elastic/fleet-server/files/12714202/elastic-agent-diagnostics-2023-09-25T10-35-16Z-00.zip)

**Screen Recording:**

https://github.com/elastic/fleet-server/assets/77374876/36bf9d94-aaa2-4454-b3f4-a0834ce95934

**Expected Result:**
Fleet Server should get back healthy itself when setup VM is turned off then re-run after sometime.