Sure, but I mean, this whole line of discussion is sort of brain-breaking. When we reason about cryptosystems, we don't generally reach the question of "how many hundreds of times can you log in before the system permanently loses all of its security". That's not like, a figure of merit in a typical cryptosystem; the right (and ordinary) answer to that question is "practically infinite".

You've picked a sort of strange hill to die on when you find yourself arguing that a system is in practical terms secure because it's unlikely you're going to log in enough times to trip the bug that coughs up your private keys. If you have to compute the number of times you can safely log in, something has gone terribly, terribly wrong.