One common problems is a plugged catalytic converter, if the engine starts fine and then starts to stall or feel like it does not have any power after running for a while it could be the catalytic converter.. the engine starts loosing power because the exhaust has nowhere to go (the catalytic converter is partially or totally plugged) Compression starts to go down causing the engine to stall or die. If you leave the car alone for a while the pressure in the engine goes out slowly thru the catalytic converter leaving the car ready to start again for a few minutes but it will shut down again.
I'd give everything a look before you start the engine and after, leave the engine for a few minutes before you start driving but it should be fine.
there are several sensors and mabe junk in your gas tank
Sounds like a plugged catalitic converter. When they heat up they block air from getting by and the engine will not run.
I would check your fuel filter...
Sounds like a fuel problem. First change the fuel filter. If the problem presists after this, look at other areas such as the fuel pump, fuel pressure regualator, etc.
Check the gas cap there is a possibility that the vent is clogged and causing a vapor lock.
Depends on the engine but severe engine damage will start to occur almost immediately. It will run a few minutes until it starts to overheat then the engine will seize. It will not take long to destroy the engine.
Dirty fuel filter.
Generally the check engine light will come on when the car is need of a tune up. It may run fine, however, the vehicle should still be inspected.
Volvo recommends premium, but it can run on regular just fine without affecting the life of the engine. In turbo models, the ECU dials back the turbo if you feed it regular, so performance will decrease, but the engine will run just fine.
Could be a Fuel Relay Switch, or even the Fuel filter itself..
It will be fine.