USB Printer intermittently works via Remote Desktop Connection

This is a follow-up to an earlier post.

- I have an HP P1102w printer connected via USB to computer A (XP SP3).  
- I connect via Remote Desktop to computer B (also XP SP3) from computer A.  
- Computer A is set up to share local resources via the RD session.  
- I installed the drivers for HP P1100-series printer and set up a logical printer on computer B named  "HP P1102w."
- Finally, I remoted into computer B from computer A using Remote Desktop, I found the logical printer HP P1102w, and played with printer ports until I could print.  Here's the important point: I used the logical printer I set up on computer B named HP P1102w.
- About 4 days later, Karen, the Computer A user calls me up because remote printing stopped working.  I take a look and HP P1102w is gone. In it's place is HP LaserJet Professional P 1102w (from COMPUTER A).  
- I figured what the heck, that's the local resource on Computer A being shared to Computer B.  It should work.
-  I check the drivers on HP LaserJet Professional P 1102w (from COMPUTER A).  They're HP P1100-series printer drivers, looks good.
- Finally I start experimenting with printer ports.  The best bets look like this:

TS0003:   COMPUTER_A: PRN9
TS0010:   COMPUTER_A: PRN8
TS0001:   Inactive TS Port

- None of these work.