It is certainly not impossible to lose height at that age. A good thing to have your doctor check for would be the onset of osteoporosis. This disease causes a loss in bone density which can lead to some shrinkage and also brittle bones. Good luck!
There are several possible factors contributing to height loss. Joint changes in feet, forward bending of the spine, and increased curvature of the hips and knees are just a few of the ways height loss can begin. Any one of them can begin in a person at any age. Nutrition and genetics may affect the age at which it begins.
People generally do not start to shrink until after age 40, though certain diseases associated with loss of bone density can cause a loss of height earlier.
Yes, it is possible. Osteoperosis can manifest at any age, much like other degenerative conditions. There may be other causes of apparent height loss, relating to diet, exercise, or even posture. If you have concerns about apparent loss of height, you should visit your doctor. Don't let your doctor dismiss your concerns. Ask for a second opinion if necessary.