Radio Cuts Out Briefly 30sec After Car Starts

[herostar]

Lately my radio has been cutting out for 2-3 seconds, approximately 30-60 seconds after the car starts. It is on the whole time, but the sounds stops. Has anyone had this issue before? Any suggestions regarding what to look at?
2005 FX35 w/ bose system (non-navigation)

 

[herostar]

Has anyone else experienced this? It's still happening and I can't figure out the cause (maybe a capacitor in the radio?). I put in a new battery but that didn't help with the issue.