Is there a loose wire somewhere (or one with some burned insulation that might be grounding itself to another in the harness) or ground? It sounds like when the recording is happening, it is heating up and the extra heat is causing it to shutdown. It could also be a "bad solder" somewhere on the board that controls the recording circuit. I have a Ford van that the radio display would go blank after a bit of use (a common issue on them). It turns out that the display circuit(s) had a "cold" solder and as it got warm, it lost contact with the board. A simple redo of the solder on the connections fixed it for good. Maybe your issue could be a common problem others have had. Did you try a google search on the item / make/ model?