I have had a couple of reservations that I cancelled where the website told me that some part of it (or all) was non-refundable. I suspect that these itineraries had a schedule change on them, because I had email notifications about such (which I ignored). Other itinearies that I canceled at the same time (and did not have a schedule change) did not have this issue.

I chatted an agent and they refunded to my credit card, per usual.

My conclusion is that there is something about a schedule change which confuses the issue and triggers the website to say it's not refundable. Annoying, but workable. (And to be fair, AA also has issues with awards that have had schedule changes -- I've had to get manual intervention to have some of those refunded. United schedule changes also would muck with the reservation back in the day. My point is, this isn't necessarily limited to Frontier, and in my experience, they do get it resolved eventually.)