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I know next to zilch about C# so I won't be much help with this review, but I can say that it looks well thought out and implements some cool features. And like retailcoder I'm still working on my version (hoping to minimize the brute-force portion) using Ruby.

If C# allows enums to implement methods, I would move CombineSolvedState into SudokuProgress. Forgive my Java syntax, but if this is allowed I expect it will be easy to translate.

public enum SudokuProgress {
 public SudokuProgress CombineSolvedState(SudokuProgress solved) {
 if (this == SudokuProgress.FAILED)
 return this;
 if (this == SudokuProgress.NO_PROGRESS)
 return solved;
 if (this == SudokuProgress.PROGRESS)
 return solved == SudokuProgress.FAILED ? solved : this;
 throw new InvalidOperationException("Invalid value for " + this);
 }
 FAILED, NO_PROGRESS, PROGRESS
}

I think this SO question addresses the issue, and one answer says it's not directly possible without using a class instead of an enum while another implies that it can be done using extensions.

Also, can't you use enums in a switch statement instead of a series of ifs?