2000 Volvo V70 air conditioning stops after a while

You need to take it in to a shop for proper diagnosis. When the A/C quits they would need to check for power to the compressor. If there is power then the A/C clutch is bad and you will need to have it replaced. If there is no power then they would need to check the electrical side for a bad relay, maybe a bad pressure switch, or worse case scenario the engine control module could be going bad. But from experiance the most likely cause is the compressor clutch. If you can, have the gap clearance measured. If it is more then 0.5mm wide then the clutch needs to be replaced and adjuted. Spec is 0.3mm to 0.5mm
Good luck and hope this helps.