Client hangs on further searches after the first one

I haven't heard of this being a widespread problem, but it may be worth you raising this with our support team for further investigation.

There is a VAF application maintained by me running in the vault so I am sort of suspicious that it could be somehow caused by it, but I can't figure out why it would be participating in the search functionality at all as I don't think there is any event triggering which would run any of my code at that specific moment when the second search is executed.

Can you disable the VAF application, restart the vault, then try again?  That'd enable you to confirm your suspicions.  Anything in the Windows Event Log?

I saw the same problem over the weekend while implementing a major change in external sources on a customer's on premise system. When the change had completed successfully I took the opportunity to update Compliance Kit, Smart Classifier, Discovery, and Property Calculator. Today I do not see the problem. So most likely it was related to one of the add-ons, but I cannot tell which one.
You should start out with making sure all add-ons are up to date. If time permits it you could update one at a time and check whether that helped. This way you can probably identify the culprit if that is important to you.

uhm, this is actually a very old phenomenon. If I remember correctly, even M-Files 9 had it. The solution is just go back to mainpage and do the search again.... Or when you cant, just right click the icon and open a new window and continue from there

Well, yesterday everything worked fine and fast! So I don't suspect my VAF anymore as I was testing and developing it several hours. My suspicion now is that when the hanging appeared, I did actually start few largish JSON-file mapping updates to some external objects (with HOT) so maybe that combined perhaps with indexing was the cause in jamming the search. It might be that it had finished all that yesterday and that's why it worked very smoothly.

So this seems to be very random problem, but I have had it every now and then and it just might be related to some HOT-update stuff (or not). When the jam happened, I was able to continue my development just by using F5 to refresh the display as that didn't jam, just had to be careful not to execute full search at any moment.

The comment from PetriJR may very well explain what I saw. The major change in external source caused updates to hundreds of thousands of objects which would affect indexing as well. When done, indexing at some point would be back to normal workload and search could respond in a timely fashion next day.