You're loosing an electrical connection somewhere after system heats up. Connection can re-establish itself after cool down.
Possibles:
1) connection between ballast terminal spade & coil wire inside it.
2) Dist. pickup coil/leads: I sure had this happen to me few years back.
Cut-out on hwy., & after some cool down time started back up.
Occurred to me 2 times before I fixed it.

That's it for now.