Huge amount of posts casues running out of memory

Hello,
I searched for answer for my problem but didn’t find something specific, so I’ll try to ask here.
I supporting blog for my costomer that posts every day several posts, and that had been for years.Posts incldudes not only text but videos, pictures, galleries of pics, etc.
Lately I’v noticed error messages in my php log that looks like that:
“PHP Fatal error: Allowed memory size of 41943040 bytes exhausted (tried to allocate 393216 bytes) in /sites/blogd2.kbb1.com/public/wp-settings.php on line 307“
When I’d checked sources I found that error occurs in function wp_clone( $object ) that called from file incudes/cache.php. Then I’d figured out that there is direct connection between amount of posts in specific categories and “fatal error”. That means if there is huge amount of posts in category you got fatal error, also on blog itself I get a blank screen with no posts.
I looks like wordpress trying to cache all the pages and fails to allocate memory.
Actually I found the solution by allocationg 96MB for wordpress.But amoun of posts is still growing and there will be time when I’ll run out of memory again, and looks like it’s gonna be soon. Is there more complex solution for my problem?

Thanks

Samuel