I get a message error "Fatal error: Maximum execution time of XX seconds exceeded in...".

This is because your server sets a limit on the time allocated for the scripts to execute. Archiving sometimes involves long computations, particularly if your site is visited a lot. If the performance of your server is low and if the execution time is limited, the archiving process may stop before it is finished.

If you have access to the php.ini file, update the time_limit parameter to a bigger value : "120" for example. Restart the web server (ie apache).

If you pay for your Web hosting service, ask your provider to change the configuration to set the maximum execution time to no less than 30s!

If he/she does not want to, consider changing for another Web hosting provider who performs better!