Can mechanical vibration during normal jogging cause brain to lose memory, even to a minor extent?

While anything is "possible" or sometimes impossible to measure, there is no research of body of scientific knowledge that would even suggest that vibration from jogging would cause memory loss. To the contrary, the aerobic exercise from jogging would more likely increase your memory by increasing the circulation and availability of oxygen to brain cells (although that is based on subjective reports and not an empirical study). The brain is well protected by the skull and by a cushion of fluid the surrounds the brain (located between the brain and the skull). The brain is self is also soft so even if there were some movement, it would not be likely to have any effect. Now, crashing your car and putting your head in harms way or getting struck in the head repeatedly (boxing) can and does cause some brain damage (e.g., traumatic brain injury in the former or simply, "punch drunk" in the later. However, if you ave having memory loss that is really noticeable, consult with your physician. it may be due to other factors.