This reply is a general comment. First, perhaps you have a Mac problem and perhaps there is a CrashPlan intersection - I can't tell based on the information provided. Next, there is a lot of advise in this thread, some of which I agree with and some that is just opinion.
More information needed: 1) What version of CrashPlan? And have you called CrashPlan - the company?
My opinions:
1) Based on several years of experience, CrashPlan ( the software system ) is rock solid and to an such an extent that I occasional wonder why it is never effected by the dozens of Java updates in a Java unfriendly world. I run a CrashPlan server and have many Crashplan client backing up to it and it is amazingly stable across many versions of Mac OS - Currently 10.5 thru 10.8 clients backing up to a CrashPlan Server..... With that said, today I am hunting for a java related instability on my Mt.Lion MacPro..... So, perhaps Crashplan is having problem......
2) All new Mac users should buy AppleCare! It is the cheapest, best tech support you will ever get. Yes, sometimes their tech support procedures and request will make you work at a problem but they are good for newer users in particular. Second, if you are close enough to a AppleStore, go to the genius bar - you will learn a lot about your Mac if you are so included.
3) Oracle and Apple need to make friends and get Java 6 and Jave 7 patches out in a timely fashion.
4) Turn off Java in your web browser. But Java is generally good otherwise.
Finally, if you a sure it is CrashPlan, or Apple contends it is CrashPlan - get help there from CrashPlan, Inc. or if you have the free version of CrashPlan, uninstall and find a supported backup method. Everyone need support sometimes and free backup is not your friend. When you need your backup you are going to need help bigtime so pay a good company and you will get good help.
I may also be able to help on specifics. But you probably are best off with Apple and CrashPlan, Inc. to start.