On Tools > Preferences > Folders I had no drives pre-selected, so I thought I would check what happened if I selected the Desktop as the site for backups. (It is a handy place to save the backups prior to Sending them to a CD/DVD or flash drive or email.)
Then I clicked File > Backup, and it brought up "Back up file to" window, where I could click the "Desktop" at "Save in" to view the list of possible destinations. If clicking on "A:" does not open the list of possible destinations, maybe your copy of PAF is too old. In that case, uninstall/remove it and install the lastest download version. Note that this will reset the Preferences to their default settings, which is often a good thing. When you run the new copy of PAF you can ask it to search for all PAF files.
Can you use File > Save As to save copies of your PAF file to other locations? If so, you can plug in the flash drive and create backups that way. With a large PAF database you cannot afford to be without good backups.
I find that having all of your backups on floppy disks is somewhat scary. I have found floppies to be less dependable than other storage media, and not nearly as convenient. (Floppies that work fine on one computer are sometimes unreadable on a different computer.)
In any case, try clicking on "A:" in the "Backup file to" window and see if that opens the list. If so, the problem is solved. If not, File > Save As, may be a better solution. With the huge storage capacity of CD/DVD and flash drives, saving space (by using File > Backup to create a compressed version of the PAF database) is no longer a priority.