I agree with everything everyone has been saying. Don't give up. This is our team's 3rd year; however, only 3 of the girls were on the team last year (our senior class had 13 girls on the team last year). So, the majority of our team is practically new. But that doesn't mean they won't do stuff. You have to find ways to motivate them. For some of our girls, it was lettering and weekly prizes. But, now that build season is happening, mostly everyone gets their hands dirty, so maybe doing those 2 things helped.
About your sponsor problem - there are many companies out there willing to sponsor teams. Its really hard to have your sponsors withdraw; however, there are ways to get new sponsors. Send out letters. Go to different companies with brochures and pictures and video clips. Call people. Or, simply, do fundraisers. Take a few of the kids that aren't "doing anything" and send them to a local grocery store on a saturday and have them bagging grocerys. They may not be helping with the robot; however, they are helping with the team. And if there are fewer kids distracted, most likely the other kids will try to help out (norms). Try some team building exercises. In my experience as a sports team captain when I was in high school, the girls that would wander off and try to do other things were just nervous. It wasn't that they weren't interested, it was they feared underperforming. When they realized that the team was there to help and make everyone better, they stepped up. In fact, some even became our best runners.
In conclusion, don't give up. Your team can do it, and if necessary, merge with another school until both schools have enough people to have their own teams.
Remember, everyone in the FIRST community is here to support you and the rest of team 2065. Good luck!