Flux Graph Inputs are being disconnected when changing tabs

### Prerequisites

- [x] I am running the latest version of ComfyUI
- [ ] I have custom nodes enabled

### What happened?

I opened the default template for Flux Klein Distilled and everything works at first but when you change tabs, and then go back to the Flux tab, some of the nodes inside are getting disconnected, not really a big deal since you can reconnect them manually or create a new template, but in my case I'm using that Flux subgraph in my personal workflow and it's annoying that it keeps getting disconnected and I need to reconnect it every single time.

I have not checked it yet if this also happens on other templates or subgraphs

### Steps to Reproduce

1.Open Flux Klein 4b Distilled
2.Check if the nodes are connected
3.Go to another workflow tab
4.Go back to Flux and check if the nodes are still connected

### How is this affecting you?

Minor inconvenience

### ComfyUI Frontend Version

1.41.21

### Browser

Chrome/Chromium

### Console Errors

```javascript

```

### Logs

```shell

```

### Additional Context

https://github.com/user-attachments/assets/cf3fdf8f-ccf8-4e8f-87ea-bf2c95d0b438

┆Issue is synchronized with this [Notion page](https://www.notion.so/Issue-10417-Flux-Graph-Inputs-are-being-disconnected-when-changing-tabs-32d6d73d3650815098f8e84e70dc2c0e) by [Unito](https://www.unito.io)