Any action or condition that requires a concentration check will disrupt the fascination and prevent the prayer attack's coup de grace, because the only relevant rule here is the class's ability description, which is very specific:

She can maintain the fascination effect by concentrating.

That means that she must maintain it (or it is lost) and that concentration is required to do so. This is a very specific rule that applies solely to the crimson assassin's Prayer Attack supernatural ability. It in no way means that other supernatural abilities either require a concentration check or can be disrupted, unless they say so, because the general rule is as you stated:

Supernatural Abilities (Su): These can’t be disrupted in combat and generally don’t provoke attacks of opportunity. They aren’t subject to spell resistance, counterspells, or dispel magic, and don’t function in antimagic areas.

Any action or condition that requires a concentration check will disrupt the fascination and prevent the prayer attack's coup de grace, because the only relevant rule here is the class's ability description, which is very specific:

She can maintain the fascination effect by concentrating.

That means that she must maintain it (or it is lost) and that concentration is required to do so. This is a very specific rule that applies solely to the crimson assassin's Prayer Attack supernatural ability. It in no way means that other supernatural abilities either require a concentration check or can be disrupted, unless they say so, because the general rule is as you stated:

Supernatural Abilities (Su): These can’t be disrupted in combat and generally don’t provoke attacks of opportunity. They aren’t subject to spell resistance, counterspells, or dispel magic, and don’t function in antimagic areas.

Edit: apologies, I of course meant "...will disrupt the fascination and prevent the prayer attack's coup de grace if the concentration check is failed, because..."