Could a large log file be the reason cron job keeps dying?
If you are talking about the MongoDB log file becoming too large you should take a look at the log rotation options here:

http://www.mongodb.org/display/DOCS/Logging#Logging-Rotatingthelogfiles

Short version - you can rotate the logs via an admin command within MongoDB or you can send a SIGUSR1 - combine with your favorite log management method and you should be good.

Something else to consider though is why the log is so large - unless it has been running for a long, long time, 15GB is a lot of logging.  You may want to make sure that you are not starting up with logging set too high (-vv etc.).  You can also check the log level with the setParameter command.  For example, to set to 0 (the default), without restarting, just issue it like this:

db.adminCommand({setParameter:1, logLevel:0})