“Is deafness with age a heriditary problem?”

Hearing loss occurs naturally as part of the aging process. However, there is much you can do to prevent hearing loss. The number one thing is to protect your ears from loud sounds by keeping your earbuds/headphones at a soft level, avoid noisy places like loud bars, nightclubs, live sporting events. If you do attend these places, use hearing protection. You can find inexpensive earplugs at the pharmacy or online.
If you work in a noisy environment, OSHA requires employers to provide hearing protection. Bring your own hearing protectors if your employer doesn't have them.
A healthy lifestyle, including a heart-healthy diet, will help keep your inner ear healthy and more resilient.

Heredity may play a factor, but for later life hearing impairment, environmental and lifetime health factors are often a greater determinant.    Angela R. Sieh Ceretto, M.A., CCC-A, FAAA Audiologist Pinnacle Audiology, LLC 6809 S. Minnesota Ave., Suite 101 605-306-4481  

It can be due to both aging and genetics; however, genetic hearing loss typically develops before 50 years. Presbycusis, hearing loss due to aging, can start to develop around 50 years or older. Other factors that can contribute to rapidly declining hearing loss at an older age would be if the individual has a history of being exposed to noise (i.e., guns, machinery, music, etc), if they have a chronic health condition (i.e. heart or kidney disease, diabetes, etc) or if they are taking medications that are toxic to the hearing system (i.e. loop diuretics, cisplatin, carboplatin). If you're concerned about developing hearing loss, I would see an audiologist and get a baseline hearing evaluation and get it rechecked every 1-2 years or sooner if you feel like you're noting changes. 
Hope that helps. 

Dr. Fling