run into problems within a couple of minutes
What Problems? From the rest of the question it sounds like you suspect multithreading to be the problem. But you didn't show any code related to that, you mentioned some default "solution patterns" for such Problems, but how can we tell if you applied them correctly?
What I can say (working with WPF and MVVM for years) that multithreading is no problem if you dispatch changes from other threads correctly.
So if your (async) method doesn't report Progress - just report back the result on the correct (GUI)-thread (by dispatching) - don't use any shared variables to make your life easy.
But I suspect you may have some other problem... because if you did something wrong with dispatching it normally won't take minutes to generate an error (or does your async method runs for that long?)
So I stop quesswork now - Show us the real error or exception - then we can try to find the reason..