I just had this happen myself. The really weird part is that the camera was sitting in its carrying case w/ all my mounts and stuff, with NO battery in it, for almost 2 months because i just moved (twice actually, long story), and i finally needed the camera again yesterday. so i put a battery in it, and no surprise, the screen showed the battery was half full - normal for it to self-discharge when not being used. but because i'd seen this thread, i checked the date. the date and time were correct, down to the minute! i never did try to sync the seconds when i first set it, because i don't need it that accurate, but the point is the date and time were right after sitting with NO battery for 2 months!
so the weird part is this - i used up a couple batteries and then charged them in my dual USB charger (not in the cam - i almost never charge them in the cam), and it was still ok even after several battery changes. but then tonight i powered up the camera (after it sat about 6 hours with no battery, while they were charging), and time/date was back to 1/1/2015 12:00. all other settings were fine - just time/date were lost. the camera currently has the 1.3 firmware on it (further evidence that i haven't used it in a while). i doubt flashing to the latest will make any difference.
i never had to take out that screw near the RTC battery - up until tonight, my camera was keeping the date/time just fine. that said, i DID take apart my git2 as part of the review process, so maybe that tweaked it enough for it to work this long?
i wasn't using it in a place where it would get a lot of vibration or shock either - it was either on a mount attached to my desk lamp (recording me making modifications to a quadcopter), and then sitting on a small box in my driveway as i tested the mods to the quadcopter. camera was not on the quad... because the quad was barely bigger than the git2 camera itself (JJRC H8 Mini)!
the night i recorded the modifications, i turned off beep and changed it from 1080p60 wide to 1080p60 narrow, and i used it on battery because i had an external mic plugged in. then the next day for recording outside, i changed it back - beep on and back to 1080p60 wide, and again used it on battery, but no external mic. nothing else was changed. it recorded correctly and had the right date/time until the battery ran out - all files are named correctly. it only lost time/date some time afterwards, with no battery installed, because both batteries were in the external charger.
tomorrow i plan to set up the camera to record a time lapse, and i will have it connected to either a USB power bank or a household phone charger to make sure it doesn't run out of power while recording. will see if it loses time/date again.