I seem to be specializing in long shots, so here goes -- I'd check the options for the three compression utilities, just in case an option has been set to use the floppy as a working location. Since most compression utilities can place entries in the right-click context menu, the activation of the context menu could cause the application to try to access the drive to see if a diskette is present.
Oh, and if you have the "Send To Any Folder" power toy installed, that can cause accessing of the floppy drive every time you initiate the context menu if it has been used to send a file to A: and the entry is still contained in the History. (You can get rid of the problem by clearing the history.) I found this out once when I used the Send To Any Folder selection for this purpose instead of the Send to Floppy selection.
I'm going to follow this with interest. This is an issue that crops up ever-once-in-a-while in message threads in various places, and ofentimes no solution shows up. Hope that's not the case with your situation. I know it can really be annoying.
Regards,
Jim