Another option, which may or may not be relevant in your case, is to run the JVM (any JVM) inside a virtual machine. Most virtual machines offer the option to store and resume state, so you should be able to restart your PC, fire up the VM when it comes back up and have the Java process pick up from where it was.
I use VMWare Player for testing on IE at work, and this works as noted above when I close and later reopen it. I don't generally do this when apps are doing anything of note in the VM, but as long as they aren't accessing any external resources (e.g. network sockets), I would expect it to work as if the VM was never shut down.
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