There are 3 ways I think the Grail's Immortality would have worked based off the Knight's warning about taking it across the seal.
1. Immortality only within a fixed bounded field
The location of the grail is within a field in which while you remain in it after drinking from the grail you are immortal. So the moment you cross the seal the immortality voids.
The trap which causes the place to cave-in may just have been a reaction to those who tried to take the grail out of the field by either warning them with a tremor to bring the grail back before it becomes useless outside the field or it was the field becoming unstable because crossing the seal means leaving the field with the grail.
With this functionality the "Price of Immortality" is to forever remain in that cave.
2. Immortality only within a mobile bounded field
The Grail itself creates a field so after drinking from it, so long as you are near to the grail you can remain immortal, the seal trap would prevent the grail from being taken outside.
With this functionality the "Price of Immortality" is to forever remain by the Grail.
3. Immortality sustained from repeated use
The most likely way would be that one has to keep drinking from the grail to retain the immortality. This would explain the Knight's state (having only been drinking water for centuries) and how Indie and his father won't be Immortals; Indie took only 1 drink and his father only had it spilled onto his wound (which probably entered his blood stream). Exactly how long the Immortality lasts until another drink is needed or if the effects wear off quicker each time is unknown. Obviously like the previous one the seal trap is to prevent it from being taken to the outside world.
With this functionality the "Price of Immortality" is to forever have to drink from the Grail.
In all the above one could get around things by making the cave your home and having people bring you stuff every day so there is the possibility that the "Price of Immortality" also included curses to the body like being unable to eat normal food so long as you are immortal.
For Indie and his father to have used the cup and not show any signs of being cursed as well could be that immortality is rendered void instantly when the Grail was lost (one could assume it was destroyed after falling from such a height or being crushed by rocks), of course the reason why Indie's father just didn't die on the spot then was probably because he was dying from blood lose from his open wound which was closed as a sort of benefit from having gained an immortal body, destruction of the grail would just strip him of immortality not revert his body to a pre-immortal state (i.e. shot and bleeding).