Is the donor hair that comes from the safe donor area or zone actually permanent or will it thin out over time as you age?

Hair taken from the donor zone is considered to be permanent and should resist the changes related to androgenetic alopecia (genetic patterned baldness), i.e. not be lost. That said, through the natural aging process, overall hair diameters may decrease over time making the donor area appear thinner.

Yes, the donor hair from the SDA (safe donor area) is permanent. These hair follicles do not miniaturize in response to DHT exposure, unlike the rest of the scalp. The basic reason for this has to do with the sensitivity of androgen protein receptors found on the follicles.
The permanent nature of the grafts from the safe donor area is the reason why these hair follicles are used in hair transplant surgery, as they will not thin or fall out due to age. 
If you are interested, I’ve provided more information about the safe donor area in the article below. At my practice, the Dr.U Hair and Skin Clinics in Los Angeles, we have observed the safe donor area to be dynamic and variable across different individuals, not a fixed region. 
By shaving the scalp, it is clear where the zone of permanent, stable hair follicles reside versus areas that are progressively being affected by miniaturization.

Do hair transplants and flap hair thin with advanced aging. Yes! At age 70-80 there is some thinning.  Having done both hair transplants and flaps for almost 50 years and followed by patients with both I can tell you that most if not all have some thinning in advanced age. Cary Grant had thinning of his hair with less density at age 70 that he did at age 40 though he had the same hairline.  There is less thinning with flaps if a properly done because there is far greater density that can be achieved with hair transplants and no texture change.