I've had such problems on previous systems. While the work was going on, suddenly the shortcuts were not working. A very simple and classic solution would be to restart the computer. In some cases, simply turning the program off and on was also helpful.
Apple and Adobe conflicts started to occur frequently. It is upsetting to have performance problems with the software hosted on Apple System and Hardware ...
Sometimes I wonder if the difference with Windovs is closing.
Sorry to hear about this. Would you mind sharing the version of the Adobe Illustrator?
Have you tried resetting preferences of the app? If not, please try doing that & let us know if it helps.
**Please note that resetting preferences will remove all the custom settings and Illustrator will launch with default settings. You can also take a backup of the folders in case you want to. Location is mentioned in the article.