Smart key issue?!

[AVMIII]

Last week smart key didn't always seem to work. Doors wouldn't unlock, etc.
Yesterday, I couldn't even start the car unless I inserted the smart key into the docking station in the dash. So, I installed a new smart key battery. Manual says plus side up, that didn't work, but plus side down does --sporadically. After work today I had to use regular key to unlock car. After driving for an hour and stopping car, it started fine with smart key undocked.
The clock must stop at times, when car is off as the time is wrong. When I start car sometimes Nav is blank for a min or two.

The car always turns over without seemingly any effort, so I'm not thinking that it is a main battery issue, although car is a 2011 with original battery.

Seems odd to me that the smart key docked always works fine, but out of the dock with a fresh battery is unreliable--if it really is just the smart key.
Oh, and I've only got one smart key.
Any ideas? Main battery? Smart key? Something else?

Power seat control was replaced last week. Could the dealer have screwed something else up?
They didn't reconnect a seat belt control and the seat is loose so who knows what else the hacks did..

 

[Buford T Justice]

Could it be any of the battery terminals in the remote?
When I changed my battery I had to rebend the metal prongs and scrape pocket gunk off the ends of them so they would make good contact with the battery.

The in-car clock being off seems odd though. Are your radio presets gone too?

 

[AVMIII]

I took it to dealer, and they tested smart key. They said that they have some gizmo that tests the output of the smart key and that it was fine. They also tested main battery, and "retightened" battery terminals. They also pronounced the main battery to be in good health. Although I asked them if anything that they could have done involving repair of the power seat could have caused this problem they replied NO. I've had the car back now for several days, and no further issues. I find it very odd too that the clock could have stopped on at least 2 separate occasions. Radio presets fine, but it probably has some sort of capacitor that stores them for a while. The clock was off by several hours in each case.

I had returned the car to the dealer to fix a rocking seat that was a result of it's partial disassembly for installation of a new power seat switch. I still wonder if this repair is the cause of further electrical problems and that the dealer may have fixed it with the latest seat repair and kept the details from me.