I have to say I get annoyed at people not moving when they are about to lose, so I think that a frame of backgammon should be over when it is mathematically impossible for one player to win.

It would also stop people from continuing to play out the game instead of resigning, as they should.

Of course if the value of the result is important and unknown (gammon/backgammon/single point) then it obviously needs to continue.