Ok, after about 3 weeks of being without it, I finally just accidentally got my SD card reader working again. You guys are going to think this is really stupid, but I will post it just in case someone else had the same problem I did...
For the 7 months that I've been using my Axim, I didn't realize that the SD card slot had an ejection mechanism. I would just push and pull the card with brute force. The problem was, when I first got the Axim, whenever I pushed on the card, nothing would happen because my fingers were too fat to make contact with only the card and not the Axim.

I concluded that my Axim didn't have an ejection mechanism because I was never able to get it to work.

Also, I've seen other devices that don't have ejection mechanisms, so I didn't think too much of it. The brute force method worked fine for 7 months, but just recently stopped working, probably due to wearing of the metal contacts.
I tried many many different things to try and get the card working again, thinking the cause was some other software or hardware problem.

I was giving up hope...
But recently, my finger nails grew out a little bit and I sort of wishfully/accidentally tried using my one of my unusually longer nails to push the card in, just to see what would happen. Wow! The card started popping in and out! And after a few tries, the card was in properly and I could read it no problem! Boy did I feel like an idiot...
But at least I'm a satisfied, relieved idiot.
Enjoy,
ApeMan
P.S. I'm not going to bite my nails anymore