Hi,
The error you have indicates that you have a fatal error of execution which stops the process. It can happen for many reasons.
The first thing to do in such case is to activate the "error reporting" and "debug mode" settings of the Joomla configuration and try again.
Then, at the bottom of the page with the issue, you should see an error message explaining what is the problem and on which line of which file the problem happened.
Now, on the export process, the most likely cause is that the process hit either the "maximum execution time" or the "memory limit" of your PHP. These are set with the memory_limit and max_execution_time settings of your php.ini
So increasing them, or reducing the amount of products to export by selecting the ones you want to export before clicking on the export button will likely solve the problem. However, without the error message, I can't say for sure.