That sounds like a threading issue. If the app tries to run a task on its main thread, and that task takes a long time (in particular, longer than expected), it could cause the UI to lock up.
Do mouse interactions still work? Does anything on the UI update at all? If not, I’d bet on a task getting stuck on the main thread.
Note that this doesn’t have to be an intense task - you may not see a CPU/network/disk spike. It could be a deadlock scenario, where multiple threads are waiting for the same resources, and each locks some, but not all of the resources. None can move forward, no work is done, everything just hangs waiting for resources locked by other threads.