By my calculations, around 2 years.

Disregarding the approximate constant drain of 5 µA while asleep, to flash the LED at 20 mA it should be:

(210 / 20) * 2000 / 24 / 365 = 2.39 years

Assuming 210 mAH from the battery, taken for 1 mS every 2 seconds (therefore you get 2000 times as long), divided by 24 hours in a day and 365 days in a year: 2.39 years.

Put it like this, it's still flashing and it started on around 12th October 2013.