Can you recover from failing the timed jump in level 3 of the original Prince of Persia?

Level 3 of Prince of Persia features a leap of faith, where to complete, one needs to press a button three screens and several jumps coming from the right. This needs a rather perfect execution.

What happens if one misses the timing? The floor plate necessary to reach the left ledge drops, making it impossible to reach the left ledge even if one runs another cycle and re-opens the door. Death would reset the plate, but is undesirable. One can technically catch the edge, but the gate closes, above.

Is a failed timing of the jump where the player caught the ledge recoverable without death?

There is no way to recover from a failed jump off this edge.

If you jump from the 'leap of faith' ledge on level three, there are two possible outcomes:

1. You fail to make the distance required to grab on to the ledge directly below the timed gate, or the gate has shut before you reach it and you are unable to grab on to the ledge at all. You either fall just short, and land in the spikes directly below, or fall down the greater fall directly to the right. Landing in the spikes kills you. Falling the greater distance to the right kills you.
2. You make the distance required to grab on to the ledge directly below the timed gate while the gate is still closing.

If you do manage to reach the ledge in time, but are unable to pull yourself up before the ledge closes, your only other option is to drop down to the ledge directly below you. This ledge contains spikes, which will instantly kill you.

Further Speculation

There are cheats in some versions of this game where you might be able to cheat death. In such cases, you might be able to drop back down to the bottom without actually dying, and return to the top for a second attempt. In such a case, you would not be able to make the jump a second time without the use of additional cheats. The tile that drops is required to give you the distance you need to make the jump; there were clearly no intentions for the player to return and attempt this jump a second time, apart from dying and restarting the level.