Nolan, I am going to try to apply common sense here, but I know that common sense and government regulations aren't typically used in the same sentence.
Common sense would dictate that you would only be required to carry E&O when you are active.
But I would hate to be the test case!
I wonder what would happen if you could not prove past coverage?
Would that mean you could never be licensed again???
Might be important to keep accurate records and pay your premium on time.
Maybe a time for "tail coverage" pun noted.
Jim