In particular, on your light switch, you will have a red wire with an orange stripe. It supplies both the low and high beam part of the switch. Check both connections and wire condition (a broken wire inside sheathing can do the same thing). Because the high beams draw more power, it can make a poor connection fail even when the low beams don't, but because both low and high don't work after the lights go out, it leads me to believe the common link (red wire with orange stripe, either wire or connections) is likely the problem. Hope this helps. There is a relay in the system, but only on the parking light side of the switch, and since they work, I'm not sure it would be the first suspect, not to mention it's in the wiring harness behind the dash (oddly not even in the wiring schematic for our year Jeep).