My eldest never slept, no matter what we did & trust me we tired it all, from crying it out (and we were right beside her in the room), to walking the roads, driving the roads at 1am to get her to sleep, pushing the buggy etc etc and she would be hanging with tiredness but she was 3.5yrs when eventually she slept.
I can count on 2 hands how many full nights we got up till then - and wouldn't need 10 fingers.
I remember saying in work we'd gotten collectively about 4hrs sleep the night before & most nights that was the case, my mgr & colleagues were shocked I hadn't fallen apart at that stage.