Assign a team to handle a crisis or large distraction
Large distractions (usually called crises) must not be allowed to stop a project, even for a short time. Let a sub-team handle the diversion, this allows the main team to keep working on the primary tasks.
There are various mechanisms for handling distractions, see SomeoneAlwaysMakesProgress for the generic approach and links to alternative specific approaches. This is a modification of SacrificeOnePerson for larger distractions, and where the distractions are long term, specific solutions similar to DayCare and MercenaryAnalyst may be appropriate.