2005 Ford F-150 Radio Failure

My radio will cut off and on while driving. It may stay on for an hour or for 2 minute it is spuratic. When the radio cuts off and I push the on/off button it displays LOW BATTERY on the radio display.

I have checked the fuse, when the failure occurs the AMP meter does not move. I do not think the battery is bad becasue the lights do not dim and there are no other symptons of low battery. The temps here are in the teens on the mornings and it cranks fine when I start it in the mornings.