Does this occur intermittently? Or is it permanently fix by toggling activation of Connections? The only thing that happens when activating/deactivating Connections is that it tells WordPress to update the permalinks rules. On activation the Connections rules are added and the opposite on deactivation. WordPress refreshes it permalinks rules simply by visiting the Settings Permalinks admin page. No changes need to be made, simply navigating to the page is sufficient to trigger WordPress to refresh the rules.
The next time this happens can you try visiting the Permalinks page and see if that fixes it too. If it does, then I would say it is a bug with EC Pro and not a conflict with Connections. Toggling the activation of Connections just happens to fix the issue.
Hope this helps! Please let me know what you learn.