One other possible solution we just found after having this issue across multiple databases/tables on the same server.
Is the max connections open to the sql server. We had an app that wasn't closing it's SQL connection and was leaving them open so we were running around 28K-31K connections (SQL Sever has a max out at 32K ish), and we noticed that once we killed a few thousand sleeping connections it took care of the error listed on this question.
The fix was to update the apps to make sure they closed their connections instead of leaving them open.