I struck out with Asus Tech Support and basically the answer was "Puond Sand".
I took the shrink wrap off my backup battery and found the makers info on it. The battery is manufactured by VARTA and the part number stamped on the button cell is V20HR. It is a single NiMH rechargable button cell, so just a watch battery would not suffice.
I found 3 sources for replacement. Mouser Electronics out of Mansfield, TX USA(
http://www.mouser.com/search/refine.aspx?Ntt=v20hr) sells the V20HR for $1.34 USD plus Shipping but their cell has no tabs on it to solder the battery leads to. It is very difficult to solder to a button cell without heat damage... Second is Farnell (
http://export.farnell.com/jsp/Electr...questid=204994) out of the UK. The price is £1.57 but they have a £20.00 minimum credit card order plus big shipping to the US. I couldn't believe the my third find, Batteries Plus (5960 Scarborough Blvd., Columbus, OH 43232 USA, 614-577-1998). Their part# is FEDV20HR - 1.2V 22MAH NiMH Button Cell for $3.99 USD and it has solder tabs already on it which makes soldering my leads to it a breeze. I was shocked to find they were less than 5 miles from my office and it was IN STOCK! I got it Friday night, soldered my leads from the original battery onto it this morning. I reassembled my Asus MyPal A716, charged it for an hour and TA DA!!!! My back-up battery now works correctly and no more Nag messages on the screen.
I hope this helps somebody else in their quest ot repair this common problem. In my internet searches, I found many other makers of PPC, especially Dell Axims to have the same issue.