I found two command line programs that might help.
First change the sleep timeout while Plugged in, to NEVER (control panel, Power Options, change plan settings), and connect the power to your Surface. Also use the kickstand to help keep airflow going around the Surface while it works.
The first one has been around for awhile, that checks the operating system files for corruption. This the first thing to try:
From an elevated command prompt (i.e. Run as Administrator), type:
SFC /SCANNOW
(this might take awhile to run, just let it do it's thing)
After that command runs, reboot, try the updated, again. If it fails the next thing to try:
From an elevated command prompt (i.e. Run as Administrator) type:
DISM /ONLINE /CLEANUP-IMAGE /RESTOREHEALTH
(Again, this one might take an hour or so to run)
Reboot when done, and try the update again.