If your toilet seat cover is falling when it should remain upright, it might be caused by a few things. Confirm that the tank cover is properly placed on the tank, towards the back.
The toilet tank itself may have shifted forward over time. Gently push it back, which should allow the seat to raise and lower normally.
Confirm that the toilet tank and bowl are level, adjusting tank bolts underneath if necessary.
If the seat is new, it may be a case of tight or loose hinges. If tight, open and close the seat and cover several times to loosen.