Apps hanging/not relaunching in macOS Catalina

I'm having a strange and pretty annoying issue with Catalina (10.15.2), on a 2019 iMac. Basically, after an indeterminate amount of time, I start getting the following weird behaviours:

- A random selection of open apps will stop responding (showing as red and saying 'not responding' in Activity Monitor, and showing 'force quit' when right-clicking their dock icon).

- Force quitting the app will work after a few tries, but I can't re-open the app. If I click its dock icon or the app itself in /Applications, the dock icon will bounce for a minute or two then stop, without the app ever launching.

- Some apps will launch and quit fine. Others won't launch at all, and others will launch, but won't quit and get stuck in the same cycle as my previous point.

- Trying to restart the iMac fails, because it tells me that an application failed to quit (one of the ones affected as described above, that isn't shown as running in either the Dock or Activity Monitor). Holding the power button to force restart the iMac fixes the issues for anything up to a few days, before the same thing happens again.

Different apps are affected each time, and they've ranged from third-party apps, to Apple apps like Safari all the way down to Terminal or System Prefs. Any ideas on what's going on would be appreciated. The Apple Hardware Test shows no issues, so I'm hoping it's a software issue, rather than SSD/RAM corruption or something like that...