What version of Access are you running and are you running some VBA code that opens files underneath a form or macro?
The business about not enough file handles indicates to me that something is opening files and not closing them. If the files were closed, you could recycle the file handles...
If this is an old enough version of Access, you also would run into the problem of having to get into the file C:\CONFIG.SYS to reset the FILES= statement to have a larger number. But that would imply like, version 2.0 of Access under Windows 3.1 or so.