Backing up logs

Question

I've been looking at my site logs recently. I have the limit of logs set to 10,000. The problem is, due to the amount of traffic we get, that number will only represent, at best, half a day of logs. Most of these are ether from access denied (I'm guessing spam bots trying to create nodes) or page not founds. The rest are items from custom modules I've built that I use to monitor how those modules are functioning (Like a notification that a queue is being run, or nodes are being created, etc.).

I've toyed with the idea of bumping the log messages to keep up to 100,000 or 1,000,000, but I'm not sure if this will cause performance issues or if it will drastically increase the size of my db.

Ultimately though, that would only really be a band-aid at best. As it would be nice to be able to keep a longer track of error messages, say weeks or months, so that I can further analyze what my site is doing, what areas need to be improved, etc. Is there any way to create a back up of log files so I don't loose them forever once they hit that ceiling?