If a state allows an auto insurance company to use age as a rating factor, which most do, then when drivers do get to a certain age their premiums can indeed increase. This is due to as you mentioned when we age our reaction time slows down and our eyesight begins to dwindle.
In fact according to the National Highway Traffic Safety Administration (NHTSA) though motorists older than 70 drive far less frequently than other age groups, they already account for an outsize proportion of fatalities. The death rate per mile traveled for drivers over 85 is four times that of the 30 to 59 age group.
The only group more dangerous than senior citizens is teenagers the NHTSA reports. Senior drivers have special trouble judging speed and distances, which causes an inordinate number of rear-end and left-hand-turn accidents.
Since insurance rates are made up in part by statistical data and risk factors, those that reach the age of 70 and above and continue to own and drive a car can see their rates go up since these mature drivers are seen as more of a risk now to their insurance carrier.
[Let CarInsurance.com help you find affordable auto insurance now.] The Florida Department of Highway Safety and Motor Vehicles (HSMV) released a 2002 study that found that seniors older than 85 pose a sharply higher risk when operating a motor vehicle. The study showed that at least 20 percent of the state's 250,000 drivers older than 85 suffered from dementia. The report also said that crash rates for drivers with cognitive dementia were 7.6 times higher than other drivers.
There is also a report about both teen and senior drivers put together by the Research and Development Branch of the California DMV. Here it shows collision rates for both sexes decline until about age 70 and then increase and the increase in at-fault fatal accidents becomes particularly dramatic at age 80 plus.
State laws and insurance company's guidelines vary so depending upon your state laws and an insurer's underwriting rules there may be a time in which a person is not insurable by the voluntary insurance market. Your father would likely not be solely judged on his age but also his driving record, and with the licensing state agency his medical record may part of their decision to keep his license valid.
There is a helpful article regarding licensing procedures for elderly drivers which can be found on the Insurance Institute for Highway Safety (IIHS) website. The IIHS article gives specific state information on state laws regarding the licensing of mature, senior drivers.
Some insurance companies offer lower rates to those between 50 and 65 years of age, since this group has lower accident rates. After age 65 rates do typically begin to rise again though and individuals over age 70 may have difficulty finding an insurer to accept them as a new customer since accidents for this age group tend to go up.
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There are auto insurance providers though that give mature driver discounts for drivers of a certain age with clean records or discounts to seniors who attend an approved driving course.
Since age is a rating factor that most states allow the age of the driver can cause rates to rise, some companies in fact will not insure any driver over 75. If his driving record has moving violations, accidents and/or claims it may be even more difficult for his to keep his insurance or find new coverage.
So your father could have trouble keeping auto insurance at his mature age depending upon the underwriting rules of his insurance provider and state laws. To find out about his state insurance laws regarding this topic contact the state's insurance regulator. | 
