>>>Sometimes the account will go to zero for unknown reasons...<<<

The two sites I have never got off 0 to start with.

Another reason to check in every few days is that often there will be a message saying no adds were found on page x but when you go to the page you will find there are adds running. However your weight will be 0. Click the validate button, the message goes away and your weight comes back.
There seem to be a couple of bugs in the system :(

If you leave it for a few days with no weight it does make a difference to your keyword positions, even with the small amount of weight I have I have noticed the difference.

Your Google API key is unique to you and all your sites, as is the adsense account.