I was thinking, maybe the problem could be caused by the USB hub, which I have connected between the PC and the Multilink. Although the hub is a certified USB hub from D-Link and theoretically should not cause problems. I just ran some tests to find out if not using the hub would solve the problem, but unfortunately (or fortunately?) I cannot reproduce the problem anymore, even with our full project. That said, I think the problem should not be in our software, because the debugger lost its connection the last time (see previous post).
I won't have the opportunity to investigate the problem in the future if it comes back, but maybe this post might help others with the same problem.