In the books red priests can continue to bring people back to life. In fact this is an entire story line the show hasn’t touched on. John Snow will probably being dying quite often. They will need the red lady around to revive him.
One death is enough for Jon. Or two, if he expires nobly at the climax. It would be cheesy, and bad writing, to keep killing and resurrecting him. It's one thing to do that for a secondary character like Lord Beric. It's another thing entirely to do it with a principal.
In Lord Beric's case, the narrative function of the repeat resurrections was to establish that bit of magic in readers' and viewers' minds so that they'll buy into it when Jon comes back. The precedent is important. But it would kill the dramatic tension if a lead character simply keeps coming back.
The bannerman in the woods can revive too
Ramsey killing his daddy
Now that you knew for sure last week
Lots of old storylines revived last nite
The Lazarus episode
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They touched on it a couple of seasons back when the Hound faced a trial by combat for murder. The guy that lost to the hound was mortally wounded, but then revived. He spoke of the red priests having brought him back from the dead, and having died many times.