Let's start with what we mean by "year-round." We in the Tri-State see goldfinches virtually every day of the year. But they may not be the same goldfinches.
While our goldfinches don't migrate, more northerly goldfinches do; and all form winter flocks that wander in search of food. How far Canadian birds migrate depends on age and sex. Female goldfinches winter farther south than males; adult males winter farther south than young males. Canadian goldfinches may leapfrog over Michigan residents, for instance, then stop to forage on seeds in our now-spent gardens before they wing into areas in the southern tier of states where goldfinches are absent in summer.
Strictly vegetarians, goldfinches surely know every edible garden seed available, including those like black-eyed Susan, purple coneflower, goldenrod, ironweed, asters, and ornamental grasses. And they know every native wild seed in shrubby areas, weedy fields, orchards, and forest edges.
The garden, now bare of the seeds goldfinches love, instead hosts little flocks of white-throated sparrows and dark-eyed juncos. They forage noisily on the ground, flipping leaves and gleaning perhaps what goldfinches, feasting on abundance, dropped and left.
Of course, other causes may alter your yard's goldfinch numbers. Autumn winds blow in an assortment of winter-only visitors, among them perhaps a sharp-shinned hawk. While mature female sharpies look very much like mature male Cooper's hawks, male sharpies are only about the size of a dove. Incredible aerialists, sharpies can roar through the yard like little jet fighter planes, taking out songsters in mid-air. Goldfinches, even in their winter olive-gray, can make an easy lunch for these little hawks.
But if goldfinches are the only birds missing from your feeders while cardinals, chickadees, and assorted sparrows continue their regular visits, a hawk is not the cause of declining goldfinch numbers.
That leads us to the third common cause for goldfinch population changes. This one has to do with what goldfinches best love to eat: thistle seed. Properly called niger seed, it's unrelated to our native Canadian thistle or non-native invasive bull thistle. Goldfinches love it for its high fat content.
But the rich fats cause us feeder hosts agony. The oily seeds readily turn rancid, and thus inedible, in temperatures over 80 degrees.
How do you know if seed has gone bad? Try this: Empty and clean feeders thoroughly. Refill with fresh seed. If goldfinches return shortly, you can assume the seed was at fault.