This particular solution isn’t one that I discovered, though unfortunately in the course of seeking a solution I neglected to bookmark the post in which I read it.
There can be many causes for an automatic repair loop, so this solution may not fix the problem for everyone.
While working on a laptop for some friends I encountered a problem after applying some Windows updates. On restart the system went into a repair loop, which resulted in an inability to restart into Windows.
In this case the problem appears to be a Windows feature that essentially makes the OS get in its own way. The solution was to Disable Early Launch Anti-malware Protection.