Remote loses connection to console

Every time I shut off my 360 I need to re-sync the remote
to the console - is this normal? is there a way to save the
setup so I don't need to do this?

Thanks, yes gamepad is what I was looking for - I will try that after I Google "guide button". I'm totally new to this and am not a gamer - I bought the 360 primarily to be a Media Center Extender.

The Guide Button is the one in the middle of the gamepad with the big X on it.

Yes, they do. The gamepad will shut itself off to conserve power after you stop using it for a while. I'm not sure exactly how long, but it seems to be around 10 minutes.

If it does it while you're in the middle of a game the Xbox will behave as if the gamepad was wired and unplugged. In other words, it will pause the game and ask you to reconnect and press Start before continuing. (As I said, just hold the Guide Button for a couple seconds to reconnect.) So no worries.

To shutdown the console or the gamepad, hold the Guide Button for 3-5 seconds and the Shut Down menu will pop-up. It's handy for shutting down the console if you don't want to get up, but it's not the fastest way to shut off the gamepad. For that just disconnect and reconnect the battery pack.