So what ever happened to Radagast the Brown?

So, what happened to Radagast the Brown?

He got distracted from his quest by the animals and birds of Middle Earth, but he didn’t actively turn to evil. The Unfinished Tales says Gandalf was the only one of the five Istari who completed his task, so far as is known (fruitless speculation about the two Blue Istari aside).

I don’t think there’s any mention of Radagast returning to the West, nor of his death. Since he can’t die of old age, was he still kicking around in the Fourth Age?