What is the burden of pleading and proving that a claim is unenforceable because it is barred by the statute of limitations?

A defendant has the burden of pleading and proving that a claim is unenforceable because it is barred by the statute of limitations. (Walton v. City of Red Bluff (1991) 2 Cal.App.4th 117, 131 ["where a claim is unenforceable the burden is on the defense to demonstrate unenforceability. When a claim is barred by the statute of limitations the issue must be pleaded as an affirmative defense"].) Thus, at the pleading stage, it was not incumbent on plaintiff to anticipate the limitations issue or plead facts relevant to that defense. Instead, defendant, as the demurring party, had the burden of demonstrating that it was a licensed or certified health care provider under section 340.5.