My team has usually only done two official events in a season; I believe it's only once that we've done three. I usually end up at around three regionals per year. Even so, there are ways to help with missing time, some of which have already been suggested:
- Don't send every person to every regional. Train people to be able to play multiple roles so that you don't have to rely on a single person for something - this way they don't have to be at all of the events.
- Go to at least one local (non-travel) competition. This eliminates extra days off for travel time. Also people can come late or leave early (do you really need 30 people there on Thursday for the practice rounds?) to eliminate the amount of schoolwork missed.
- Plan competition dates strategically. Don't plan your events two weeks in a row if possible. It's easier to make up missed work if it's spread out, rather than missing several days of school two weeks in a row. Also, try to find an event that overlaps with time off from school, like spring break, a holiday day off, or a teacher inservice day
- Notify teachers about absences and ask for work in advance. They're more likely to be understanding if they have notice, and it will be easier for you to make up the work before you leave rather than on Sunday night when you get back exhausted from not sleeping for three days. We all know that no one actually sleeps when they're at robotics competitions.
I went to three regionals this year and only missed three classes in total. It's possible to manage robotics and your school work!