So let's break out the data! Woot!
Wikipedia has a handy list of popes, including age at election and age at end of papacy (for whatever reason). In addition, there is a page on the oldest popes - whether at election or at the end of the papacy (and usually, life).
If you check that second link, you'll see that when Benedict XVI retires, he'll be a year older than John Paul II was when he died.
You need some numbers? Okey dokey.
Below is a histogram of papal ages at election, starting in the 15th century (to go back to the last time a pope resigned) and papal ages at end of papacy. I have included B16 in both graphs, highlighting the bar he is in (or will be in) in red.
Do you notice anything? Yes. He's on the upper end.
Jesus, Joseph, and Mary, can't an old man retire to a convent and be left alone?
Now, B16 may have years of life left to him (checking my handy-dandy mortality calculator that I always keep open, using an optimistic mortality table (developed for U.S. annuitants and includes very generous mortality improvement) – life expectancy of an 85-year-old man is about 8 years. Of course, he's almost 86, but I disabled my calculator to allow calculations that high because that end of the mortality table is unreliable).
But morbidity tells — just considering one item, senile dementia, rapidly increases in incidence as people get older – especially past age 85. That may not be his issue, and I don't particularly care to know about whatever health problems he has. That's his business, especially once he retires.
I wonder how many of these "papal truthers" could do their jobs (if they have any) into their mid-80s.
In any case, I hope the Pope can enjoy a well-earned rest, however long that may be. Viva Papa!