This is kind of weird behavior: I pin an application to my taskbar. About 5 minutes later I get a bsod. When I reboot, the icon that I pinned to the taskbar is unpinned. Do these changes - to the taskbar - get saved into memory and then upon shutdown get written to the drive?
It is, as far as I know, quite normal for Windows to 'lose' the settings upon an unexpected reboot or shutdown. The same would happen if you run a 'Force shutdown' command.
The next time you boot up your Windows PC, try just moving an icon and then running the following command:
Now move the icon again, but this time reboot by pressing "Start" and selecting "reboot" from the 'shutdown'-selection menu. Upon the PC booting up again, the icon should in fact not have moved, and remain where you left it on the desktop.
If you have ever logged into a domain, and then logged out again, and read what Windows said it was doing, one of the things Windows said it did was "saving your personal preferences" (or 'settings' or something similar - I only know what it says in Danish: "Gemmer dine personlige indstillinger"). If it is unexpectedly shut down (as it is by a BSOD), it won't save these personal settings.
The Geek-site "How-To Geek" has a great article explaining BSOD's, why they occur, how to troubleshoot them (should you wish to), etc. - you can find it here: http://www.howtogeek.com/163452/everything-you-need-to-know-about-the-blue-screen-of-death/ (at least I find it to be great).