You could say either, I can't make it to the class is probably better. When you say for, it can suggest that you will arrive later. for instance, i wont make it for dinner, but i will see you in the bar later. you could even say, i can't make the class.

Both are correct and make sense for the context. Maybe some of these would help you clarify things. I cannot make it until tomorrow (hay que esperar haste mañana). I cannot make it for four (la implicación es que hay una plaza, quizá puedo llegar a las cinco). I cannot make it at two (no puedo asistir a las dos específicamente, quizá antes o después pero no a esta hora).

If you're talking about an object (for a project for example) then you would say "for". If you're talking about being able to attend the class then you say "to".

i think both