SQL Server distribution database log file grows uncontrollably after full database backup
It sounds like you have a high volume of transactions happening with your replication. If so, that "clean up: distribution" job should probably be running far more often. It sounds to me like it's happening once a day. On my high transaction replication server I have it running every 15 minutes to keep just the latest 36 hours. That way it paces itself and doesn't bog down.

Here's an article that might help - http://www.sqlservergeeks.com/blogs/singhsatnam84/sql-server-bi/563/sql-server-controlling-growth-of-a-distribution-database