When hell prevails

I've discussed whether there's a tipping-point for Catholics. Is there anything representatives of their denomination can do to falsify Catholicism? 

Catholic apologists like to say the gates of hell can't prevail against "the Church". but we could turn that around: if the gates of hell do prevail against the church of Rome, then there's is not the church Christ founded. That promise doesn't apply to their sect. 

However, a Catholic might counter that my objection is inconsistent: what's the tipping-point for me?

It depends in part on the level of the comparison. Are we talking about alternatives to Christianity or alternatives within Christianity? To evoke the web of belief, not all my theological beliefs are equally central. I could conceivably change some of my theological beliefs. That would entail some adjustments in my overall belief-system. But it would still be Christian.

It also depends on whether there are viable alternatives, superior alternatives, alternatives with some evidence. You can't change positions in a vacuum. If there's no available fallback position, then there's no room for change. 

In addition, I can't pretend to approach such comparisons as a blank slate. I'm already pretty familiar with the alternatives, as well as the pros and cons for each alternative.