I see nothing in your Report that gives me a clue to the cause.
Whenever I have unusual behavior like this, I reboot in Safe mode, then restart normally.
Safe mode startup is a very useful fix-almost-all-OS-problems tool. It does a Repair disk during the boot process, and is faster than booting from an external drive to run DU-Repair Disk on the internal drive.
Disk Utility is an app native to the OS. When it or any other native app misbehaves, you should concentrate your repair efforts on the OS. When booting in Safe mode, all 3rd party additions are "disconnected", and only the base functions of the OS are activated.
My second effort at fixing this problem would be to re-install the latest Combo update. This will do a similar thing - revert any intentional or inadvertent changes to the OS back to the default state, without affecting your data and most settings.
Third, if you have a relatively current external backup clone, you might try booting in that drive to see if the DU problem persists. If the problem is not there, you can clone that drive to the internal drive and restore current data from Time Machine.
Those folks that are Terminal-savvy may offer better solutions.
Hope this helps.
Fusion uses lock files to prevent multiple processes from modifying the same files at the same time, as could happen if you tried to run to copies of Fusion (say version 3 and version 4) at once. When Fusion quit abnormally, as it did when your laptop battery died, it left behind the lock files and you need to clean them up manually.
See this support article for how to clean up Fusion lock files. If that doesn't solve it, do a Spotlight search including system files for files whose names end in .lck and if they look like they belong to Fusion, delete them.
Best Answer
The first thing is to get into the console app / system log and trace the shutdown cause and timing of the restarts. Then you would look to see if there are hangs or crashes in /Library/Logs/DiagnosticReports prior to those events.
Depending on your interest in scripting shell to collect matches from log files, here’s an example of using those log files to find events like needles in a very large, long and confusing haystack.
Most likely, you will see a pattern (or see there is no pattern once you get 25 restarts logged and cataloged) and can remove the hardware, software or look into what is the logged reason.