here's an odd thought. could the batteries be bad? it sounds like the phone is charging the batteries, but not fully. once the phone detects that the battery has dropped below a certain charge (in mAh), it will assume that the battery may die at any moment and shuts itself down to prevent data loss.
the problem you are describing would be either a) the batteries are at the end of their life or b) the phone is not recognizing the proper amount of charge. if the batteries were at the end of their usable life, the phone would charge them to their highest capacity and then maintain the charge. the problem with this is that if the batteries were only accepting a minimum charge, then they would appear full while actually not being charged.
the standard batteries i have laying around say they're 1500mAh batteries. if these batteries were only charging to 500mAh, then they would appear to the charging circuitry to be "full" but the system would report them as about to die.
on xda-developers, there is a link to an app that would show you the actual charge left on the battery in mAh. you might want to look into this to see if the batteries are EOL.
Lithium Ion batteries have a general cycle where they will lose approximately 20% of their capacity every year.
Definitions: mAh= milliAmphour: energy capacity of a battery
EOL= End of Life