UPDATE: Well, this is weird. I fixed it by entering today's date (it defaulted to 01/01/1990 so for testing I just put in 05/01/1990). Thought it would start at the earliest time it could store but I guess not. =/

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Ok, so basically it seems that everything else in the BIOS on this board saves even without the CMOS battery, but I've been trying for probably an hour and can't get the time to save! I've of course changed out the battery, but it still acts as if there isn't one in it at all. Here is everything I've tried:

Checked the battery with a multimeter, it's good.
Checked the battery holder's pins with a multimeter, it's good.
bent the pins on the battery holder to make 100% certain it's making a good connection.
checked the BIOS configuration pins to make sure the jumper is in the correct location
unplugging the computer and plugging it back in
reflowing the solder on the connectors with a soldering iron, and even adding slightly more solder.

I'm really stumped here. Any ideas would be greatly appreciated.