I got a new finch feeder last year and the finches quit coming

Try some different food. Sometimes bird food gets some mold in it and they will not eat it. I don't get many finches - but I have had this happen with other birds.

They are migratory birds, where do you live? Try different food. Even the type of feeder can make a difference. Look into "fly through" style feeders. Even my breed of finches eat sunflower seeds and black oil sunflower seeds. Keep the food fresh, if it gets stale or moldy they know not to eat.

I have the flip side problem. Mine will eat me out of house and home. I can easily go through 10 pounds of seed per day year round.

Check these out!

Mine are much simpler, if you want photos, let me know!

Here is a good article about the placement of feeders. We have ours next to a flower bed away from our house and fence. That way we have less trouble with squirrels fighting them for the feed, and we can see them from the patio. https://www.thespruce.com/bird-feeder-placement-386532

Is it possible that the mixed food won't fit through the holes in your feeder? Some feeders are made just for nyjer. If they can't get any seed they will stop coming.

My finches love my suet feeders the best

are your feeders clean and can the seed get out properly? if they are then use more niger seed at first then cut back on it also they make a finch seed that has some niger in it but other things finches seem to like