Based on documented evidence, at what age would someone normally expect to see his chess results start to decline?
According to this study chess grandmasters peak at age 31.4.
This study confuses the hell out of me, but there is one sensible chart at page 20, that seems to indicate that you can still improve a little bit in your thirties and generally hold your playing level into your mid-forties. After that the decline becomes noticable.
The slight discrepancy between these two studies is easily explained by the fact that the first only looks at grandmasters, whereas the second examines more than 40,000 players. In fact I would assume that the very top players peak even earlier these days.
I found a very good chess.com article about this topic. This guy analysed more than 71,000 players and found a rating peak in the late twenties. Until you are eighty you'll lose 200 Elo points on average, which really isn't all that much.
There are many exceptions of people performing on a high (and sometimes higher level than before) when they get older. The most obvious are: Boris Gelfand who reached a World Championship match in his forties, Vishy Anand who is currently World No 2 and in his forties, Victor Korchnoi, who reached two World Championship matches in his forties, and many others on the amateur scale. Even at 80 depending on the level you play at there may be room for improvement. It might be worth looking up a coach.