I've noticed lately (maybe the last couple of months), playing as Pyro, that sometimes I'll light a demoman on fire and he doesn't suffer any afterburn. As soon as I stop hitting him with flames, they go out. Is there some new Demoman item or something that is causing this? I'm quite sure they are not being extinguished by a teammate or by picking up a health pack.
The Chargin' Targe adds an immunity to afterburn effect. You can still light them on fire, but they will be extinguished as if they were a pyro. This was changed in the patch on July 10, 2013: