I'd rule it that if the defender can't Fall Back, you can't press the attack in the first place. And in other situations where the conditions allow the maneuvers, that are initiated, and then the Attack, movement, or anything else becomes impossible, you just lose the action (or whatever). You can't Press the Attack unless both you and your target have a speed of 5' or greater, but the maneuvers involved don't take any of either of your movements.
The point I'm seeing here is that this is about a movement motivating series of blows. You are stepping forward at your target while swinging, trying to force them back.
So if someone is grappled or unconscious, no Press the Attack allowed.
If there is a wall behind them, it screws up the trajectory of the maneuver and it can't happen. If you don't know it (lets say you can't see the wall) you have already committed to attacking. You lose your bonus action and you Attack normally without the benefits or penalties of Press the Attack.
If they can move back but don't want to, that is them choosing not to Fall Back, which means they awkwardly try to hold you off, which gives you the expertise die and other elements of Press the Attack.
You can Press the Attack at someone by a cliff, since they can choose to Fall Back right off the cliff, and everything works as normal. If for some unusual reason they do Fall Back and fall off, you lose your Attack. But you just got them to jump off a cliff so it wasn't a wasn't really a waste. If they Fall Back and can fly, you can go ahead and make your attacks at them, since they are still within your reach.
I would probably allow you to choose not to follow them, but then you lose the Attack (and of course your action because it was committed) while still taking the penalties from Press the Attack.