I think the cold snaps we have had could affect your banana tree. The very tropical ones don't handle the cold well. Also if your tree was a pup and removed from the mother it might be struggling a bit. I have found that banana trees are pretty resilient. Try not to overwater and give it some time. Hopefully you will see a green leaf developing at the top of your tree. Once it gets established, they are heavy feeders, so some fertilizer after it recovers well may help.

What temperature zone are you in ? i am in SW Florida on the 9b/10a border and near the Gulf of Mexico. Have 6 total banana pups going, 4 in the ground and 2 in pots,..all are goldfingers, a plant that has decent cold tolerance.
I fertilize these guys about once a month with a small amount of 6 - 6 - 6 and water them every other day when there's no rain. To someone not familiar, they might look stressed out as there is some black on each, but I am confident they are doing fine. We've only had about 5 nights in January when I've had to bring the potted ones inside.
IMHO, I think we are almost home,..have seen the worst ( hereabouts anyway ) of the cold nights. If your banana plant has made it this far, hopefully it'll survive another 3, 4 weeks till all danger of below 40 temps disappear. Good luck !