Pay up front:
For; you get a discount probably. Great!
Against;
If you find flying isn't for you. Tough!
If you want to change flight school. Tough!
You are unable to continue through a change in your own circumstances. Tough!
If the school goes bust -loads do. Tough!
You have a complaint that "trial flighters" take precedence over you because your money is in the bank and the trial flighter's isn't. Tough!
One of life's rules is don't lend money to anybody or pay up front any sum of money which would be painful for you if you didn't get it back. But human quest for a "bargain" dictates that some do and will continue to pay up front.
Number Cruncher,
Other than that, other indicators of its ability to continue as a going concern would be how long it’s been around and the amount of aircraft it operates.
Remember SFT at Bournemouth? The problem is that schools usually don't actually own the aircraft, they are owned by a holding company, a separate company or the bank even.