Do you have the PHP logs enabled in php.ini (check key error_log)?
If so, please check to see if there are any resource-exhaustion FATALs there. These would be consistent with the random interrupted executions (even if it’s the bug’s fault that it is taking too long). At least, seeing the messages there would be a diagnosis.
Other things that might be interfering: SELinux restrictions; ownership/permissions issues, .htaccess issues.
(I am just spitting out ideas so that, in case one doesn’t help, you can try the other one)