I'm losing the sensitivity in my fingertips. I drop things, like keys or containers. My doctor says it's just aging. Is it? I have arthritis.

Numbness & weakness. You may have cervical radiculopathy, which is the compression of the cervical nerve roots due to disc protrusions or osteophytes (bone spurs) in the neural foramen (side holes) where the nerves exit the spinal canal. It you may have peripheral nerve entrapments such as carpal tunnel syndrome. You may consider seeing another physician or ask your doctor for referral to see a neurologist.
Not just aging! You likely have carpal tunnel syndrome (cts), which causes pain, numbness and tingling in the fingers. In advanced cases, the tips of the thumb, index, long and 1/2 of the ring finger can become so numb, that using your hands becomes difficult. It is common to drop objects or be unable to button clothes, or grip objects. See a board certified orthopaedic hand surgeon for evaluation and treatment.