Have a look at the following article. I don't know if it will help but it's worth a try.
According to the author, the problem is that your system core file size is set to 0.
http://sysadmin.carlusgg.com/?p=197
That top part seems to be half the solution. The rest of the solution is to create a folder for Core Dumps and add the directory to httpd.conf
Follow this tutorial:
http://www.cyberciti.biz/tips/configure-apache-web-server-for-core-dump.html
Edit: None of the above solutions have solved it for me, actually. Maybe it will work for you.
I recently tried changing the owner of the /etc/apache2 folder to www-data. It's lessened the number of signal segmentation faults, but hasn't solved it.
Edit from 2020: The above (changing the /etc/apache2 folder owner to www-data) is not a good idea in practice.
Have you tried using gdb to trace the problem. See the following thread:
"[notice] child pid XXXX exit signal Segmentation fault (11)" in apache error.log
Edit: I placed Nginx in front of Apache and I am no longer receiving segmentation faults in the Apache error log. I also think the configuration is a better implementation then Apache on its own. I know it's not a direct solution to the problem but if the segmentation faults are difficult to trace and causing problems, it may be worth implementing this solution.