After experiencing this problem for weeks, with the Centura's clock resetting itself (usually within hours of my setting it right) to -5 hours of Eastern Time, I'd been sufficiently inconvenienced to come here and read through all of this discussion (and one other) — little of which gave me hope the issue could be overcome. Nonetheless, over a weekend, I tried any idea which sounded remotely plausible. Most techniques provided no lasting fix, as documented by others here. But eventually, after I'd about given up, I got the clock working correctly.
My clock has kept perfect time for a week now. [fingers crossed]
Alas, I can't say for a certainty which trick (or combination of them) fixed it. Nor can I rule out the possibility that the now perfect time is a coincidence. But in the hope that this info might help someone else, here are the last few things I did, after which the clock has worked properly:
1) Installed and setup the ClockSync app, in rootless mode.
http://play.google.com/store/apps/details?id=ru.org.amip.ClockSync
Given that no app can automatically reset the time on a phone (like mine) which has not been rooted, it does not seem like this should have fixed the problem. I installed ClockSync thinking that it would at least alert me when the clock was wrong. After setting my Preferences, I used its option to "sync manually with ClockSync help". In the week since, my phone's system time has remained perfectly in sync with "atomic time" (pool.ntp.org).
2) After previously and repeatedly trying every variation of Date & Time settings (in the system settings), I went back to my normal preference:
√ Automatic date & time
√ Automatic time zone
In the Location services settings, I have also enabled (only):
√ GPS satellites
3) On a whim, I disabled the 24-hour format in the phone's Date & Time settings. I personally prefer 24-hour time, and my phone had been set to use it since the day I bought it. This is the first time I've ever disabled it. I cannot think of any logical reason why this setting should make a difference — but than, this unresolved bug has defied logic.
If anyone duplicates any or all of these steps, with or without a positive result, I'd be curious to hear about it.
If the original problem recurs, I'll come back here to post an update.