I think it is pretty impossible to reach a state were you can't progress anymore. But it is possible to reach a state, were you just think: This is not fun anymore, I want to do something different.
Exactly. Developers never make an impossible game. The testers will catch that.
They may not catch something tedious because, after testing the same things for the hundredth time, it will be pure meta-gaming and it probably gets tedious for them either way.
