It's not the age of the battery as much as the number of charge cycles and whether it has been abused (regularly running the battery down until it dies is abuse - that will shorten the life of the battery). It also depends on details of the battery design, so there are no guarantees that what's true for one model will necessarily be the same for another.
But with a modern lithium battery I'd expect about 80% of capacity to be left (a common measure of lifetime) after serval hundred, or maybe 1000, cycles. So if the battery only just does a day for you, so you are getting 1 cycle per day at the start, then somewhere around 2 years (very approximately) it probably won't last a day with the same usage. If you are only using 60% per day when you start then it will still get you through the day at the same age, both because you had more margin to start and because charging from 40% to 100% is only 0.6 of a cycle. Plus, as noted above, running it flat will degrade capacity faster than if you recharge when it's only partially depleted.
My HTC One is about 2 years old, and while there has been some loss of capacity I'd say it's still got about 90% of its original runtime.
