A suggestion I'd have, if even just for a year to keep your team from dieing and being harder to restart next year... there are a ton of teams within a 20 mile radius of you guys (which probably makes it hard for sponsorship)... but you could always try to work something out with the other teams to do a temporary merger for a year to keep new students joining if you can't find funding. Maybe even some of those teams will have sponsors who are interested in wanting to sponsor yet another team. You have many teams very very close to you guys and several in the same town even, talk to them and see how you guys can help each other out. That's the whole purpose of FIRST... Gracious Professionalism.
Good luck, and if you need any help, feel free to contact me.
-Mike