It will depend upon state laws if you will need to start the time period which you must keep future proof of financial responsibility (the SR-22) over again or get to resume where you left off before the cancellation of your first SR22.

It is true that typically it has to be a 3 year continuous period, so if it lapses you have to start over again. We have heard of situations where DMVs or Judges don't require this, but in general you have to start over.

In many states your 3 year period restarts after you reinstate a policy with a SR-22 filed with the state.

Washington State for instance states that whenever any person whose proof has been canceled applies for a license within a period of three years from the date proof was originally required, any such application shall be refused unless the applicant shall reestablish such proof for the remainder of such three-year period. 

In Texas, once the Texas Department of Public Safety (DPS) receives notification from the insurance company that the policy is cancelled, terminated, or lapses appropriate enforcement action may be taken. If the SR-22 is still required and there is not a valid SR-22 on file, the driving privilege and vehicle registration is suspended. If the person establishes financial responsibility for the remainder of the two-year period beginning on the date the evidence of financial responsibility was required.

Since there are some states that may require you to restart the whole period over again so check with your state's Department of Motor Vehicles to see what is required of you with regards to the time period in which you must carry the SR-22.