Your question: "I seem to lose power to the clock in my 1996 jeep overnight while sitting. I would have to reset it everyday when I get into it. I recently replaced the vehicle battery. Worked fine after replacing the battery. After about three weeks, I'm having the same ..."

Your situation does not make any logical sense to me. It would seem that the clock should work as long as it's connected to the battery. The only variable that I can think to check is the voltage in the battery. It could be that your alternator is not charging the battery to a high enough voltage to maintain the clock. Check your battery voltage with the engine off. It should be around 12-12.5 volts. With the engine running, it should be around 13.5-14.5 volts. If the volts are good, perhaps you have a bad clock.

I would think the clock itself is bad, the engine wouldn't start if the battery was low enough to not maintain an lcd.