If they're not up now, they probably didn't make it through their first winter. It's not an unusual situation, even in peonies. Winters can be very hard on new unestablished plants. If they haven't died outright, the primary buds may have died and dormant ones may be enlarging now to take over.

So there's a possibility they may recover? Should I leave them in the ground?

I had a similar thing happen to some iris plants and a bleeding heart. Healthy plants, lots of blooms, died back to the ground, and then just never came back. I also had some lily of the valley I planted last year never show up again. And I've heard people complain that you can't kill lily of the valley.

Of the six peonies I've planted in the past two years, only three have survived. That's expensive, considering how pricey peonies can be.

One of my second-year peonies, my Bowl of Beauty, has a small flower bud. I am so thrilled! But still nothing out of the two dead-looking ones.

I've had better luck here in CO with early spring planting. It gives them time to establish good root system before heading into winter.

Sometimes when peonies are damaged, in my case several people stepped on them before they emerged, they will wait a year before sending out new shoots.

I am very glad that your wait was successful.