I think the dead battery is a correct assumption, when your turning it on and off normally you are most likely using the power button on the front of the ps3, however when you jailbreak you have to cut the power completely. With a dead battery there is nothing allowing it to hold the time when you do that. Replace the battery and all should be well.
sounds like its definitely the battery, a new one is only a few quid and its an easy enough job to connect a new one.
careful though sony have soldered the positive & negative leads to the original battery, only disconnect it if you have some insulating tape to hold the connections on with or obviously a soldering iron.
should really be easier to get at the battery though its really buried in there.
I have a CECHG01 ps3, it has a new battery in it and it is not soldered (never was). I replaced it after it recently ylod for the 2nd time (I thought it was the battery too). From what I can tell it only loses time if you jailbreak it, if you power it off and back on without jailbreaking it keeps time perfectly. The battery holder was the same as on any motherboard it appeared.
well if you're sure it's not the battery and never happens without the jailbreak (not even once) and happens with different payloads (not even one works) its obviously the minimus, return it for a new one.