Thinkpad 365x Ext Diskette Problem

Have you tried running IBM's diagnostic utility? To get to it, you
need to enter the setup while booting. I don't remember if you have to
hold down the f1 key or the esc key while booting. I think it is f1.
With the floppy drive connected, run the diagnostic test on the entire
system.  For some reason, the test with show two floppy drives on the
computer, but only one will be tested. This is correct.  (I think the
other one is if the computer has a built in floppy instead of CD ROM).

Another thing to try is to go into device manager and remove the
floppy drive controller, restart the system and let Windows re-detect
and install it.

I'm still baffled as to why your floppy is configured as the b drive.

I've had my floppy drive replaced twice on my 365xd due to problems
similar to yours. Twice I had problems similar to yours that weren't
related to a hardware problem. Once it was corrected when the floppy
drive controller was removed and reinstalled. The second time it was a
conflict with some anti-virus software (I believe it was Mcafee Virus
Scan). That was solved by going to Norton (or a newer version of
VirusScan).  

Incidentally, I don't work for IBM nor am I a tech support person.
I've owned a Thinkpad 365 for  2 1/2 years so my suggestions are from
experience.

Hope this helps.

Bob