Maybe a stupid question but have you tried another USB stick?
We use USB sticks from 1GB to 32 GB in size for transferring files to/from a couple of win 7 machines that a client uses and have never see any problems. They were all setup using DFSee to provide the LVM information and drive letter and also do the FAT32 formatting.
It's a FAT USB stick, so with a limited capacity. Clients can be yet another reason to fix it, because you don't want to be known for returning or delivering "damaged" drives. FAT32 isn't always an option, for example when an old FAT MP3 player is used.
Two images of the drive have been shipped to dfsee.com by now, and both files (same size) were different. Don't expect anything, but let's hope that some command can set OS/2's vritual "NumberOfEAs" bit from 0 to Windows' virtual "IsFlushed"-bit to 1.
If the average user of Windows gets used to answering Yes/Okay when an OS/2-drive is used, then one day this user may format your HPFS backup drive instead of CHKDSK'ing a FAT file transfer drive.
I could use a FAT32 drive for a test, but I'm not sure that OS/2 can access my device, and your test is as good as mine.
To reproduce, obvious steps excluded, FAT is classic FAT (FAT16): Use Windows 7 to save a FAT file, e.g. INVOICES.ZIP. Remove the USB FAT drive "safely". Boot eCS, use CMD.EXE to both "COPY x:\INVOICES.ZIP y:\" and "DEL x:INVOICES.ZIP". Remove the drive, and (try to) repeat the first step.
your stick might be suffering from dead cells that the wear levelling isn't fixing.
I cannot exclude anything, albeit I can use another, different FAT drive for testing purposes. The "IsFlushed"-bit is just a story too. BTW, I couldn't use an internet example to set or unset Windows flushing the drive. Perhaps that doesn't work with FAT. I'm using whatever the default setting is, and I'm used to manual flushing anyway. There drive is as old as 256 MB USB flash drives, but isn't iused that frequently. The images were produced with an "empty" drive (which still may include dead cells).
I do hope it's something like the usual DIRTY-bit of a drive, hence the "IsFlushed"-story. If so, then a command can be used to set it right for victims of Microsoft again. You don't want a client complaining about a damaged drive and/or a possible virus after you've borrowed their drive.