Q: Is there a civil rights violation when there is a continuous deprivation of a protected property; a driver's license?

A: I think you are confusing some concepts in law -- and that's okay as you are not a lawyer. When defendants assert a statute of limitations as a defense, there are two doctrines that may be to plaintiffs to avoid the defense and thereby extend the time during which claims may be brought: (1) discovery rule (a limitations period does not begin until the plaintiff knew or should have known of facts giving rise to the violation) and (2) continuing violation doctrine (plaintiff may recover for acts which, if viewed individually, would be time-barred, by treating them as part of a pattern of violations or as a single violation).

You asked if there is a civil rights violation when someone is deprived of a driver's license. Maybe, but it does not have anything to do with these defenses to the argument that a person's claim is barred by a statute of limitations.

With that said, one would need to know more about why the license was not granted to begin to assess whether you can sue to redress the harm. Last year, the ACLU did bring suit for a "court’s practice of suspending the driver’s licenses of people who are too poor to pay exorbitant traffic fines. In 2015, over 11,000 driver’s licenses were suspended in Solano County for failure to pay alone." Note, however, that this lawsuit was described as a first of its kind, which means that they are attempting to make new law.

https://www.aclunc.org/news/ca-legal-orgs-bring-first-its-kind-lawsuit-challenging-harmful-driver-s-license-suspension

Here is more information on the issue of suspending licenses in California if you are interested: http://www.lccr.com/not-just-ferguson-problem-how-traffic-courts-drive-inequality-in-california/