I just wanted to inform you guys about the solution to my problem.
In summary, the problem seemed to be a C++ / QML-engine interfacing and memory management issue:
I was lucky enough to identify a small set of candidate revisions of the software which potentially caused the described behavior. In these changes, there was noticeable that in the QML/Javascript code there was a lot of manual fiddling with list models. For example, specific list-model entries (provided by the C++ core) were accessed via ListModel.get(), and they were in turn stored as static property values. I assumed that this is dangerous because as soon as the C++ core deletes the list model entries, it is not guaranteed that the references stored within the QML engine are properly cleared.
Therefore, I modified this part of the implementation, and suddenly the application was running perfectly stable again.