Nice touch offering the December rent break. I guess it's just like offering incentives to good employees to generate loyalty and keep them around for the longterm. I am sure there is great worth in offering this small incentive to a tenant you want to keep, even if you could be charging more to a new tenant. Aside from the cost and effort of finding a new tenant, knowing that you have a consistent, paying renter that will take care of your investment is ideal.
My parents have a small, older rental house that they charge less than market rate for, as they have never increased the rent for the current tenant who has lived there for several years. They have had renters trash the place before, and they know getting a little less from a good renter is a preferred scenario.