Table top players realize a single die roll can change a good/bad situation instantly. When a DM has multiple rolls it being used to create tension like the Nettie situation. If the tension isn't there, multiple rolls are being used because a DM wanted a different outcome but the player either rolled too good or too poorly. Never let something really important be decided by the dice alone. Meaning, a DM shouldn't let something occur in which only the dice can get a player out of. The player needs to make several mistakes on their own and perhaps that one last die roll determines their fate.
In this case the player did make multiple mistakes though?
They casually told a healer that they have a illithid tadpole in their body.
They followed said healer to a secluded room.
They let the healer slash them with the *cough* antidote.
Prior to the last point the players could back out and escape the 'were fucked' situation and walk off.
The implementation needs work but the situation here is something that does warrant multiple tests. It just needs to be tweaked to make sense and be more forgiving. Its insane in its current implementation...