what were you running? sounds like you might want to bring other options, build your champs a bit differently 

point of fact there is a cut-off; 1 hour or 1500 turns

is there a paragon mob at that stage?

faction wars bannerlord flavor against the first big guy. My bannerlord team is very weak and I haven't optimized giscard so I watched him slug it out solo against the big guy on auto*2. what surprised me was the way the AI created a stalemate situation hence even after 30 minutes they were still slugging it out

There's actually a 1-hour cutoff? That's new o_O

Not sure if this is what you are after but I have used a Shadowkin champ called Jurogin.  He has a skill called True Smite which ignores Unkillable and Block Damage buffs.  He has saved me from getting stuck a bunch of times, also works on Paragon.  Just have to cycle him to hit at the right time.

Often I just place him as part of my crew in the Doom Tower, since you never know when an unkillable or block damage might show up.