I agree, this doesn't sound so much like a battery issue as a processor issue.
The battery life times listed in this thread are a bit deceiving. I have several Logix55xx style processors that have had batteries lasting a couple years or more. These are systems that are not powered up 24/7. It depends on how much memory, environmental conditions, and how long and often the system is powered down.
The 63 days quoted above is how long an L55 processor at 25 degrees C will maintain a program when powered down 100% of the time. This is not a case of "you get to buy a new battery every 63 days".
In RSLogix5000 go to Help=>Online Books==>ControlLogix Manuals. Select the ControlLogix System User Manual and look at page 405 (25-3) for a table that shows a battery life estimation tool. The one mentioned above is worst case only, which is also part of the manual I mentioned.
Try your batteries in another processor, try another processor. The battery appears to be the symptom, not the cause.
OG