Argan kernels, fruits regurgitated by goats, are 30% cheaper than the regular kernels used to prepare food argan oil. The use of such argan kernels as a cosmetic ingredient, after refining, is thus economically attractive. The oxidative stability of argan oil prepared from sub-quality kernels is not known. In the present paper, the physicochemical quality, oxidative stability indices, and bioactive compounds of refined argan oil (RAO) obtained from sub-quality kernels and virgin argan oil (VAO) were compared and evaluated over a period of storage of 12 weeks at 60 °C. Quality parameters consisted of free fatty acids (FFAs), peroxide value (PV), p-anisidine value (p-AV), UV extinction coefficients (K232 and K270), total oxidation, iodine and saponification values, induction time, fatty acid composition, and tocopherol content. Our outcomes reveal that the combined effects of refining and storage generally resulted in high values of the routinely measured quality indices, including FFA, p-AV, K270, K232, and PV. Likewise, refining reduced the levels of individual tocopherols and unsaturated fatty acids (USFAs) but increased saturated fatty acids (SFAs). Similar trends were observed under storage with decreased levels of tocopherols and high SFA for both RAO and VAO. Storage also resulted in an increased level of USFAs in the case of RAO but not in VAO. The obtained results show that RAO was more sensitive to oxidation than VAO. At room temperature, RAO had a shorter induction time of six months, implying that RAO will have a shorter shelf life compared to VAR. Thus, such instability means that the refining process for argan oil must be carried out with great care, and this oil needs to be protected once refined.