Solution: Where did the Years Go?

Answer: TIED UP IN A BOA

Between the mention of Years and the fact that there are 12 feeders, solvers should hopefully think to look at the Chinese Zodiac. Each answer can have a single letter replaced by a Zodiac animal to get a new word/phrase. (The best break-ins seem to be IMAGINE US or NEE.) Ordering by Zodiac order and taking the replaced letters gives the meta answer, TIED UP IN A BOA.

Feeder Answer with Year Replaced Replaced Letter Notes
CUTE CURATE T
DELPHI DELPHOX I
BANE BANTIGER E A mountain in the Alps
DICE RABBIT ICE D Also known as a frost flower
IMAGINE US IMAGINE DRAGONS U
ORANGE PEEL ORANGE SNAKE EEL P
HOLI HOL HORSE I From JoJo's Bizarre Adventure
NEE GOATEE N
ASPHERE MONKEYSPHERE A
BROCK ROOSTER ROCK B An obelisk in a state park of the same name
NABOO NABDOGO O
AEON PIGEON A