TT and charging
If your lighter socket is controlled with your key, then it is not being charged unless the car is on. Watch the green LED upper left to see. A good indicator is that when you start your car, the TT also comes on. If you leave the TT on when you exit your car and the lighter power is off, you will be running on internal battery alone. I recently had a rental car for a few days and was always having to remember to turn the TT off when I left the car for extended periods of time as the socket in it was controlled by the key. Many folks, like me, have lighters that stay on even when the car is off, so the 4 hour thing really doesn't hold much clout. As for putting the TT in the home dock every 3 weeks, that's more for software and GPS QuickFix updates than anything electrical.