I had my dahlia tubers in flats in a bit of soil, after wintering them in a cool shed. Many (nearly 5 dozen) now have sprouted and I've potted them up. But I'm running out of space, and started checking out the remaining tubers--many have new roots, but no sign of eyes or shoots. Should I toss them, or keep waiting? My Feb-April plant room is actually our music room for the rest of the year, and my long-suffering family is a bit impatient! Plus, our cat keeps trying to sleep on the flats...

Not every tuber will develop an eye. Some are "blind". I've found that when I placed tubers on top of the soil to sprout, the crown of the tuber would sometimes dry out and get a bit hard. I've had far better luck getting them to sprout by putting 6-8 into a gallon zip lock with barely damp soil. I've had many that never sprouted but still grew those hair roots.

^ What Dan said! Blind tubers still develop roots, despite not having an eye to grow with. Not sure where you're growing, but I'm in Nebraska, and I'm giving my "even the losers" 2-3 more weeks before they meet the compost bin!

So, when you next go to divide your tubers, try to give each one as much stem material as possible. Eyes won't develop on the shoulders or necks. As you've observed, they are alive, and they will put out roots, but foliage will just never happen without last year's stem. A lot of growers mark up the stems with sharpie before they start cutting to make sure each tuber has an eye. Often an eye will develop where none was visible as long as there's an appropriate spot.

I put non productive tubers on a flat of damp soil. I check them periodically if nothing happens they become part of the compost bin.