OH3 Model and Things go "offline" after a while, when I configure the system

By bridge do you mean the event bus? If so see the following for OH 3:

Or just MQTT Event Bus [4.0.0.0;4.9.9.9] for OH 4.

There are lots of ways you could be doing this and the steps you take may be relevant. Please describe step by step what you’ve done up to the problem manifesting.

At a minimum it can help us reproduce the problem.