"...until my task is done..."

[HerenIstarion]

Radagast got overly interested in the intricacies of bird and animal feed

Since Radagast was specially chosen by Yavanna (and forced upon Saruman for the company), it may be presumed that that was the main idea of sending him along, though it be in contradiction with

Indeed, of all the Istari, one only remained faithful, and he was the last-comer. For Radagast, the fourth, became enamoured of the many beasts and birds that dwelt in Middle-earth, and forsook Elves and Men, and spent his days among the wild creatures. Thus he got his name (which is in the tongue of Numenor of old, and signifies, it is said, "tender of beasts").

Unfinished Tales