Premature end of script headers: index.php

Hi, I’d like to know how big can get the wordpress database so the script would run flawlessly?! I suspect that is the database size (>300mb) that give this error “Premature end of script headers: index.php”, Error 500.
I’ve tried to increase the php memory limit, the mysql execution time but nothing seems to work. I have no idea what to do.
I have other wordpress sites on my server, smaller databases, and those are running just fine. I don’t know if is the script or the server that cannot handle the database size (if the database is the problem).
Any advice is appreciated.
Thank you!