In a civil case, unless a federal statute or these rules provide otherwise, the party against whom a presumption is directed has the burden of producing evidence to rebut the presumption. But this rule does not shift the burden of persuasion, which remains on the party who had it originally.
Initially, the plaintiff has the burden of pleading with sufficiency to state a claim. This then creates a presumption that the claim is true.
Under the bursting bubble theory, a presumption vanishes upon the introduction of any evidence which would support the nonexistence of the assumed fact. Such a claim would then fail summary judgment.
The bursting bubble theory is followed by the Federal Rules of Evidence, but courts usually do not follow the rule for being unfair to parties with presumptions. They do this by raising the bar of sufficiency for evidence to support the presumption's non-existence, usually sending it to a jury.
The sufficiency required is almost a preponderance of the evidence, but courts do not raise it quite that high because that would shift the burden of persuasion, violating FRE 301.
The "Professor Morgan" approach would say just shift the burden of persuasion, but this is not followed by any court.