What type of switch are you using?
Is the ANT signal too strong and is pissing off the receivers enough to just shut down like that?
What if you plug the wire into the ANT jack. Take off the multiplexer and plug that coax right into the ANT. If the receiver and switch are working correctly you should be able to get ANT signal.
Now try plugging that same thing into the SAT. Does SAT work?
If those two work than the problem would be closer to the box, possibly in the multiplexer. The receiver should be able to use the appropriate line signal for each input even if their is no multiplexer.
If you are able to plug the line right from the switch into the box for ANT and get ANT channels and into SAT and get SAT channels i would think your multiplexer is screwing with you. If plugging the line right into the ANT does not give you ANT stations or the SAT does not give you SAT channels maybe the switch is bad.
Did this just start recently? Did you make any additions to your system and then this started?
I can't imagine both boxes going out at the same time like that, my guess is something else, like a bad switch or pair of multiplexor's, but two multiplexor's failing at the same time would be quite convenient as well..............