I agree with tim, When you actually engage with sponsors within your area they have been known to respond better.
I would suggest letting them get to know your team and see the finish product that you have put your hard work and their money into.
Engaged students are always the best. When they see the passion that students have for STEM and learning it rubs off on them. These are the type of employees that they would like to see come back after their education.
Creating relationships is very important. When doing this it could honestly be a breaking point or turning point for your school. This is ultimately what teams either struggle with or excel at when courting sponsors. Also I think realizing that even if they are not going to sponsor or level of sponsorship has changed, does not mean it is the end of the relationship. Make sure that you keep every alleyway open, you never know when it may come back to help you.
Something really cool that we did one year was a special diamond studded picture frame for our sponsors. It was a bit to heavy to actually throw away with out actually thinking about it.
Those are a bit of tidbits I have picked up through out the years. If you are more personable as a sponsor you may be able to create a relationship through out the years!
Be creative and good luck!