I've been riding track for 4 seasons now and have run off the track ONCE, and that was because I was in a tank slapper and physically could not control the bike to make the turn. Making the corner is almost always and option, and if you are running off once per trackday you need to take a step back and calm down before you hurt yourself. You should never be scared out there, take it easy, work on the fundamentals and getting comfortable, if you are always running around the track scared you are:
1) A danger to yourself and others,
2) Not going to learn as quickly because you wont be concentrating on improving, but rather gritting your teeth ever corner wondering if you're going to make it.
3) Not doing something right, either not looking through the corner, or don't have confidence in either yourself or the bike.
Only you can Identify what the problem is, why are you standing it up and running off, once you know why you're doing it, figure out the fix. No confidence in the tires? Get new tires. No confidence in the bike? Get the bike fixed or looked at by someone you trust. Ttarget fixating? Go slower and focus on picking up your visual reference marks and looking through the corners. Riding over your head? Slow down.
Next time out, make it priority 1 to keep yourself and your bike under control all day, this means no running off the track.