To answer this question,
This can be a script or plugin that is consuming too much memory.
What is the memory_limit value in your php.ini settings?
if it is below 64M or 128M, try increasing it to 64M or 128M
If you don't have access to PHP.ini try adding this to a .htaccess file: php_value memory_limit 64M
if that does not solve the issue, try removing q2a plugins 1 after the other and moniter your error log.
What does your error log says? you can see the specific script eating all your memory in the error log located in the root of your site example cpanel ---> file manager ---> public_html ----> error_log
Open that file and check the entries. You will see whats really wrong