I just learnt that I can log all commands in the console, and when doing this I get the following output:
Writing file /C/path/to/file.cfm with encoding UTF-8
So, nothing extraordinary as far as I can see.
Also, following the behaviour for the last day or so, it does seem a lot more random than first described: It's not just the last opened file that closes (although it sometimes is) but it also frequently happens that all files except the currently active one get closed. Anything in between these two extremes is possible, really, and I haven't been able to detect and order in what is getting closed and what isn't.
Finally, I noticed that it seems that the file(s) to be closed receive focus for the fraction of a second before actually closing. This is hard to verify as it happens too quickly for the buffer to actually update, but the tab representing the file changes colour as if it was active for the fraction of a second before disappearing, and the buffer flashes quickly. As I said: this is so very fast that I wouldn't absolutely say it happens, but it seems to be the case.
As I said, any help would really be greatly appreciated, as I spent quite some time setting my installation up, and therefore don't really want to start again from scratch ...
Thanks for taking the time to read this!