The rules don't say anything about this, but I was wondering if it's possible to auto jump when FTL control is down.

Damage to a location prevents you from using that location, but with the auto jump nobody is using the location, so yes you can auto jump. In fact you have to when prompted by a crisis card.

Hey there, just wanted to confirm this. The issue recently came up in our 5th or 6th game, and there was quite a bit of discussion. I didn't see the issue mentioned in the rules or the FAQ. Does anyone else have thoughts on this?

I can just agrea with Frakking Baltar. The autojump doesn't involve activating the FTL location, and damage to a location only disables activating it. It doesn't alter any game mechanics.

Yes, you still auto jump.

Logically, one could infer that since the FTL controls are damaged, the Galactica would be unable to jump under any circumstances until the location is repaired. However, the rules explain how to handle each situation and they are exclusive of one another. As smuggler wrote, it doesn't alter any game mechanics.

For damaged locations, the rules state Characters may move into a damaged location, but may not use the action listed on it (until repaired by an engineering card).

When the drawn crisis card has the prepare for jump icon the fleet token moves one space ahead on the Jump Preparation Track. If this causes the token to move to the auto jump space, the fleet jumps to a new location.

Yes, you still jump. No, it doesn't really make sense thematically.

Thanks for the clarification. Just to seal the deal, this is from Corey Konieczka:

Yes, the token still advances, and the ship can still Autojump.

I hope this answers your question!
-Corey Konieczka
Fantasy Flight Games
Design and Development

It's allso added to the FAQ now. Great work FFG and Corey