Check your php config.
make sure mem limit is set to max 256 or lower, as long as your site loads, its enough, try going doen as low as possible.
if you set max mem limit in php to say 1024M even with 32 meg if you can only have about 25 php processes at same time so if you get 30 hits at same time on your server it will run out of memory.
if you can set it to 64M you can have 512 phpp processes at same time
Tweaking a server takes some time, there is enough to be found on optimizing a cpanel server.
installing engitron will unload your server as wel if fully optimized, engitron gives great information on tuning a cpanel server.
