Hi Scott,
I haven't seen any problems like this. If you have enabled cache of Joomla or any other cache extension, you can try to disable them to see if the problem is gone.
CMGroupBuying asks Joomla to not cache it by default, you can check your components/com_cmgroupbuying/controller.php to ensure that $cachable is not set to "true". However, third party cache extensions may try to cache everything.
If you use services like Cloudflare, you can exclude your shopping cart or any pages which stores user's information to see if it helps. If your server or hosting provider has any kind of caching, you may want to disable them to see if there is any differences.
Regards,
Hung