We had this same problem with a bunch of our E6510s. We decided to start removing some of the latest windows patches around the time that it started happening. We seem to be having some success removing KB2529073 and KB982018.
Same issue with dell 6320. We found it to be the WWAN card(model Gobi 5530) while docked causing the ASF2 Force Off. Disable the Wireless Switch on the right hand side of the computer. BTW: ASF stands for Alert Standard Format controls features such as WOL. Hopefully, this helps you.
i think this has to do with a power issues.
Dell e6510 have loose batterie units so when picked up or put down, will restart/shutdown for safety
I had the same problem!
The solution was easy and kind of stupid! My Dell laptop has a bit of loose battery module. The battery wiggles around a tiny bit and I realized it is when I move the laptop, it shuts down! I put a piece of folded paper between the battery and the laptop, on the opposite side of the battery connections so that the battery is pushed against the connections. Then I put the battery back so that the battery module is fit and snug. Now everything works well! No reboots or shutdowns anymore!