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Robust LaTeX commands are either “naturally robust” — meaning that they never need \protect, or “self-protected” — meaning that they have \protect built in to their definition in some way. Self-protected commands, and fragile commands with \protection are only robust in a context where the \protect mechanism is properly handled. The body of an \edef definition doesn’t handle \protect properly, since \edef is a TeX primitive rather than a LaTeX command.

This problem is resolved by a LaTeX internal command \protected@edef, which does the job of \edef while keeping the \protect mechanism working. There’s a corresponding \protected@xdef which does the job of \xdef.

Of course, these commands need to be tended carefully, since they’re internal: see ’@’ in control sequence names.