Whenever I hit the save button in a product, it is removed from all categories that it is currently in. We migrated from Magento 1.9 to 2.1 recently, and this issue has been happening consistently on every product.
I checked and no errors are being logged to exception.log or system.log, the debug.log has several cache_invalidate messages, but I believe that shouldn't be related to the problem.
Even after saving a product once, if you save it again after re-adding it to the categories, it gets kicked out of them again.
Any ideas where to begin troubleshooting this?