Celery tasks suddenly stop executing, nodes can't find each other
Navigating to /var/log/rabbitmq/rabbit@[server-name].log and scrolling back to when the issue first occurred led me to this message Disk free space limit now exceeded. Free bytes:999378944 Limit:1000000000. 
Turns out the hard drive was filled to the brim, which was causing all sorts of trouble for RabbitMQ and Celery, it seems. Freeing up space resolved all issues entirely.
I have one master server and 6 worker servers (each with a couple workers running on them). All of a sudden, after many months of flawless execution, all of the tasks stopped getting executed, even though there were no code changes. Now, even after rebooting all the servers involved, restarting RabbitMQ, restarting the workers, etc, it appears as though the servers aren't able to find each other, and thus no tasks can be completed.
When I run celery -A proj inspect active, the response is Error: No nodes replied within time constraint. I'm also able to connect to the broker using Flower, but it lists no workers, even though the workers are running and pointing to the same broker. On the master server, which is in charge of adding tasks, my application now appears to hang indefinitely on apply_async.
In my application, I have the broker set to pyamqp, and the backend set to rpc:
Celery('proj', broker='pyamqp://[master server's IP]', backend='rpc://[master server's IP]')
I feel like I'm missing something really simple, but I can't figure out what it is.