They can be arrested at any time for treason and other felonies. In fact:
"The Court concluded that the Framers' use of the identical phrase, without any explanation, indicated that Congress's privilege was to have the same limitation regarding criminal actions as did the parliamentary privilege from which the language was borrowed. The clause, therefore, does not provide Congress with any immunity from criminal prosecution."
heritage.org/constitution/#!/articles/1/essays/26/privilege-from-arrest