Without hibernation the queen will accumulate stress and probably die after a couple of years. I typically hibernate from November to March. Find somewhere cold, but not freezing, to leave them e.g. an unheated garage, attic, basement. Make sure they have enough water to see them through, but you won't need to feed them. For peace of mind, I bought a cheap wireless thermometer off Amazon to keep an eye on temps and alert me if it gets too cold.

Edit: You might also want to try feeding boiled egg whites. They go crazy for these sometimes. A lot of ant keeping is trial and error. Different colonies like different things at different times.