Sorry for late entry to this thread. For us robotics is a year-round endeavor. We don't necessarily go beyond the robots, but we definitely go beyond the tournament. We’re involved with FVC, so some of our opportunities will be a bit different than those of FRC teams. However, I believe that FRC teams can benefit from is purchasing some Vex parts and using them to practice and prototype. Our calendar of last year looked like:
July- August
Fundraise for, drool over, select, and purchase Vex kits (50% off!)
Student: Discover a Vex hobbyist only 1-hour away. Visit and pester him for good ideas.
Mentor: Troll for interest in an FVC Championship. Attend planning meetings. Pester contacts to start/join a Vex team.
Sept.-Nov.
Begin meetings. Train students. Watch them come and go. Train more students.
Mentor FLL teams. Coordinate and volunteer for FLL tournament.
Begin work on FVC Challenge.
Plan events for local start-up FVC teams. (never came to fruition

)
Dec.-Feb
Attend a scrimmage
Serious work on the robot.
E-mail teams met at FVC scrimmage with questions & suggestions.
Troll various Vex forums to gather information in preparation for competition.
March-April
Attend local Championship event. Advance to Atlanta.
Fundraise. Tweak robot.
Atlanta!
May-June
Assist another FVC team with their event for recruiting rookies to Vex.
Troll the internet for new ideas and designs.
Meet as a team in members’ homes to build from ideas on internet.
Invite another team to meet in our home to build from ideas on internet.
Assist at Vex demo at County fair.
Basically, if there is one very enthusiastic person (could this be you?!) who is willing to find various opportunities, the other members will often join in when invited. The further you're willing to travel (we often go 2 or more hours away), the more opportunities you'll find. The more contact you have with other teams and people in the community, the easier it is to see how being in FIRST is more than just the robot, even though the robot is what brings you together in the first place.