“Deaths from falls may have increased because older people are living longer, living longer independently, and are living longer with chronic conditions,” said Elizabeth Burns, a study co-author and health scientist at the U.S. Centers for Disease Control and Prevention’s injury center.

She noted that some medications also make older adults prone to falls. That includes prescription drugs affecting balance. Burns said research shows their use of certain psychiatric medications that can cause drowsiness and vision problems has increased substantially in recent years.
I doubt if the increase is due to living longer, I suspect it's much more likely to be caused by over-medication. Especially BP and anti-cholesterol medications. Neil Postman got it wrong, we're not "amusing ourselves to death" we're being medicated to death.