We were playing against Cthulhu; wakes up and a discussion began. The text reads:

Dreams of Madness - While Cthulhu stirs in his slumber , investigators have their maximum Sanity and maximum Stamina reduced by 1.

So, one of the guys i play with thinks that becauses Cthulhu awakes, then this efect no longer applies, so the investigators must begin the final battle with their ORIGINAL maximum sanity and maximum stamina.

What do you think?

If I remember correctly, the "while X stirs in his/her slumber" abilities is supposed to last the entire game even when the AO wakes up. It sort of makes sence thematicaly; the AO isn't very likely to lose some of their powers when they wake up.
I think there is another thread about it somewhere.

Yes, Tbla is right, the "stirring in his slumber" effects last also during final battle.