Communications error breaks Jetpack's Activity Log rewind feature

I ran into an issue with one of my sites (no longer in existence) when trying to rewind. All the rewind buttons were greyed out. @thingalon, @singerb, and others looked into it without finding much. I happened to check the wp-admin Jetpack debug page and saw there was a communications error. No one had any suggestions that helped me fix it in a way that would be easy for a user to fix (sorry, but deleting the options table is not easy).

I thought it was maybe a one-off issue with a Pressable test site, but then it appeared again on [Rick's site](test.whoisrick.com). If it's happening more than once, it could happen to others. **This is a big deal** since we need our product to reliably be able to back up in crisis.

At the very least, we should be able to fix it. Maybe it's time we built that button to remove/reset the JP options table and turn JP off and on?