I'm thinking THATGUY is on the right track. It sounds like your well's pressure switch is set to 30-50. 50 is fine for sprinklers, unfortunately 30 sucks. More on that in a minute.
You say the rotors pop up fine sometimes. Thats because by chance the pressure tank is charged to somewhere near 50 PSI. Even if your system pressure drops now the rotors will stay up because it takes much less pressure to keep them up then it does to pop them up.
The times that they don't pop up your pressure tank is charged below 40 PSI because maybe you flushed a toilet or used a sink and drew some water out of the tank, but not enough to cycle the pump on. (your manually turning on the system, and then off again triggers the pump to come on and build pressure so when you turn it on the second time you have enough pressure built up to pop up the heads) So when your rotors come on and the pressure is 31 PSI, ideally the pump would cycle on and build pressure to over 40 PSI and your rotors will pop up all the way, maybe a bit delayed but they would pop up. In your case it sounds like the pump is unable to build pressure back up to 40PSI. If you can't maintain 40 PSI with the rotors on, well, you've got yourself a real problem. You need to have less rotors on a zone. (This is a problem with sprinklers on a well. Knowing your static pressure and your GPM is not enough to build a system. You need to know how much water you can get at a constant 40PSI or better. You seem to know what type of pump you have. Can you find or do you know the pressure curve for it?? )
Okay, back to what I was saying about 30-50 pressure switches sucking for irrigation. Adjust the pressure switch limits to 37-57. That is probably the max you will be able to adjust it to. See if that fixes the pop up problem.
Also make ABSOLUTELY SURE your pump can build pressure to 57 PSI to reach cutoff both initially and after you have run your irrigation system. If it can't you cannot use 57 as your top limit. Your pump will burn up in a matter of minutes if it can't reach cutoff when no water is being used. If you intend to leave it at 37-57 you need to add air to your pressure tank for the best pump performance (see sticky at the top of the well forum on how to do this).
Even if this fixes the pop up problem running the irrigation system on less than 40 PSI is less then ideal even if it seems to work. I would increase the pressure switch settings and decrease the number of rotors on a zone until I could achieve a constant 40 PSI or better.
-rick