FOUND IT!
I use a batch file to build the app. There, after the compiling and linking, I use OPTEDIT with it's EXTRAMIN argument like this:
OPTEDIT MYAPP.EXE -EXTRAMIN 40000
Reducing this 40000 solved the problem.
Now, I only have to see if I can remember why I made it that high. It had something to do with building a VERY large index file, and I made the EXTRAMIN higher every now and then when I got problems as the index file got bigger. But I'm sure that a lower figure will do fine. Anyway, I could alwways run my app on the server with a lower value for EXTRAMIN (and avoid the index building there), while keeping the higher value on the W98, XP stations as long as they're happy.
In all, I think this may be interesting for anyone who uses OPTEDIT in a batch file and then forget all about it (like I did). When problems arrive, go back to your building batch file and reconsider!
Thanks GriffMG and TonHu for your help. All your response pushed me into experimenting untill I found the problem and that was all I needded.