The max level for protection is the same as every other enchant, 32k, and it keeps taking more damage the higher it gets, it doesn't stop, although it may get to the point where you don't take any damage except for extremely high level swords
All enchantments are limited to a maximum of 20 "enchantment protection factor" points, giving 80% damage reduction - anything above this will have no further effect and it is reached with a full set of Protection 5 or a single piece with Protection 20 (the total EPF for regular Protection is the same as the enchantment levels on all pieces added up; the damage-specific forms have 2-3 EPF per level):
When a player or mob wearing armor is subjected to damage, the EPFs of all applicable enchantments are added together, capped at 20, and then damage is reduced as damage = damage * (1 - (cappedEPF / 25)), giving a maximum reduction of 80% at EPF 20.
Because of the caps in the calculation, it is possible to achieve maximum protection against specific types of damage with just three pieces of armor. For example, two pieces of armor with Blast Protection IV (EPF 8 each) and a single piece with Protection IV (EPF 4) would give a total EPF of 20 versus explosions. Any additional EPF would be wasted against explosions (but might be useful against other types of damage, if applicable).
The only way to completely negate (most) damage is with Resistance V, which reduces damage by 100%; otherwise, the most you can get with armor is 96% (80% from full diamond or netherite armor plus 80% of the remaining 20% from enchantments) and in practice this will be less due to armor penetration unless you modify the "armor toughness" attribute to be near-infinite (or play in a version prior to 1.9, but then enchantments are randomized to between 50-100% of the maximum, rounded up to the next 4%, giving as little as 52% damage reduction with 25 EPF (in these versions full Protection IV was 20 EPF or 40-80% and the limit was 25 EPF, capped to 80% after randomizing).