Alt. 1:  Some command makes it do this.  E.g. you
might have an AV app loaded that has been preset
to check the floppy once a week or once a month.
Alt. 2:  Transient electrical fault in the floppy drive.

Possibly a program was installed from the floppy drive and now it searches for
it. Usually you can just put that floppy in, rerun the program and then properly
switch to another drive 'before' removing the floppy.

Clear your recent Documents list on the Start Menu.

Turn off the option in your anti-virus to check the floppy drive.

Delete all references to A:\ in the Registry, usually found under Most Recently Used
(MRU) entries:
Click Start>Run, type scanregw and click OK.
When it asks if you want to back up the registry, click yes.
Click Start>Run, type regedit and click OK.
Click the Edit menu> Find, type in A:\ for what to look for, check the boxes for
Values and Data for where to look, and click Find.  Right-click on the A:\ data
where found, and click Delete from the menu that appears.
Press F3 to continue searching, till done.
Close the Registry Editor.

Look in C:\Windows\Pif folder (or equivalent if you installed Windows to a folder of
a different name), and remove any shortcut whose target points to the A:\ or B:\
drive.