If you connected a busy repo to Reviewable, you may have run into a situation where it used up all your GitHub API quota and both you and the repo connection were stuck until it replenished. As of a couple weeks ago this should no longer happen! Reviewable will now try to avoid using more than 80% of your hourly quota, and automatically switch to using the credentials of other repo admins (who have signed in to the app) when your quota is getting low.
I'm still tweaking the algorithm for corner cases and to account for GitHub's undocumented burst quota limits, so you may get occasional spurious warnings about event processing being delayed but overall things should be much better. Don't hesitate to get in touch if you have any questions, though!