ssh_exchange_identification: Connection closed by remote host (BB-10785)

I have a cron job that pulls from a bitbucket repository once an hour. Every so often, the cron job emails me

ssh_exchange_identification: Connection closed by remote host
fatal: The remote end hung up unexpectedly

This started a few weeks ago with this happening perhaps once every few days. Now it's getting worse, happening almost every hour.

To check, I set up the same cron job on a completely separate host, and it's showing the same behavior. So I suspect the problem is on the server's end.