If it makes you feel any better, our school district cut our entrance fee ($4k) from the school budget due to financial difficulties. However, they had no trouble ponying up $20k to send our cheerleading squad to a national competition.
The problem with most schools is they are so used to accomodating athletic programs, they have trouble acknowledging "that club that tinkers with battlebots" can be educational. What you need to do is ensure your district understands what exactly FIRST is all about. Show them your robot, ramble off some gear ratios and pneumatic pressures, and trace your electrical system for them. Let them know you learned more in the 6 weeks of FIRST than you have in your entire school year (without saying it like that of course
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They can't give a program either a monetary or educational value until they realize what the program is all about. Invite some board of education members to your build sessions, invite your mayor or selectmen, your superintendant, and principal. Invite them to competitions, make them know it's a lifechanging experience, in a very positive way!!