Thanks!
Okay, so I started debugging, but once in a while the error was gone, which meant there was nothing wrong with the plugin. I tried to increase the memory limit in the wp-config.php file, and it resolved the issue.
The PHP process was running out of memory, there was only a few KB left when ajax search pro started to initialize. I left the following code in the wp-config.php file:
ini_set('memory_limit','512M');
It should be okay now.