There is no restriction in the PDF stamper plugin as to how big a file can be. Basically, you can stamp file of any size.
Now, when the file is big it is expected that the script will run for a longer time as it has to go through every page and stamp it. Looks like your server is killing the script as it's taking longer than the "Maximum PHP execution time" allowed by your server.
All you should need to do is change this execution timeout value to a slightly higher value so it doesn't timeout. The maximum PHP execution timeout value is specified in your PHP.ini file of the server. It's best to contact your hosting provider to do this if you are not familiar with it.