The longest I ever kept one for was a year and a half. Mind you it got squished by a rock slide so it could have lasted longer.
But the other 5 I have tried over the years they lasted about a year or less before they started going down hill and one day they were gone. I got 2 out of 5 to eat prepared foods and the ones that ate a lot of live foods lasted longer for me. Keep in mind I have fish that are older then 20 years so a year and a half is not great to say the least for me in terms of fish life. Nowadays I stay away from these fish with specialized diets requirements because I believe if you can't keep a fish long term and it is destined to die in captivity I don't keep them. Especially if it would have lived longer in the ocean.
As to how long they live I personally don't know anyone that kept them that outlasted 2 years. But likely someone has. Based on my experience in keeping fish, for the size of the mandarins I should have been able to keep them for at least 6 to 10 years or more. Because of the way I run my tank as I foster the food web aggressively, fish last a long time in my tank as they get lots of live nutritious foods on top of prepared foods. I am a veteran reefer and if I can't keep them long that is saying something about the specialized needs of these fish. With that being said if you are experienced reefer and are willing to put a lot of time and effort to keep these fish you will up the chances of success.
If people want to up the chances of success try some of the DIY feeding rings that seem to work well.
http://www.saltwatersmarts.com/diy-target-feeder-mandarinfish-pipefish-2804/
Some good reading on picky feeders as well.
http://www.saltwatersmarts.com/keeping-difficult-marine-fish-3898/