post.php and memory use

I was wondering if post.php requires more memory or other resources as the number of posts on a blog grows? The blog in question has got over 10000 posts.

I keep getting blank white pages when editing existing posts or publishing new ones. If I turn off a plugin the problem stops. Then the next day, when another 25-50 posts are added, I have the same problem again. I turn off another plugin, and it stops…and the next day it repeats. Now I can’t turn more plugins off, because the only ones left are really needed.

I don’t understand it at all and can’t find anything matching my problem.

There is nothing in any logs.