> Could it be that an overflow happens (because the page is 
> really really really huge)?
I doubt this can be the problem.
Did you try restarting the mirror? ("Continue an 
interrupted mirror")

> How can I limit the scope of the mirror?
Using filters (scan rules) : Set Options / Scan rules
Such as
-* +www.yoursite.com/section1/* +*.gif +*.jpg +*.png +*.js 
+*.css