[deserth3]

I've read what you said several times and I can't overcome the feeling this guy is blowing some smoke up your ass. Or at least trying to sound smarter than he is.
First I'm assuming you have a factory radio with XM.

Second 4 milliamps isn't ****. That's only .004 amps. Very little for a component that's connected to a 10 or 20 amp fuse.

Third; A high resistance connection is quite possible. But you should be able to feel the heat if you touch the connector. But you will have a voltage drop across it. i.e. 12.5 volts instead of 13. Maybe even more of a drop. And yes total amp for that circuit will increase, but that will only run down the battery faster or burn up some wiring. The system will be more affected my low voltage.

Forth; Do you live in Northern Utah? I'd really like to take a look. Pm me if you do.

Fifth. At least take a picture of this supposed bad connection and post it. If you can.

But changing the connector won't hurt anything.