While I don't know the specifics of your situation one possibility is that you uninstalled an old version after installing JMP 19? On Windows, file associations are stored in the registry with very loose ownership. Basically, the most recent application to register as the handler for ".jmp", for example, wins (gets to be associated). In a related behavior, if you uninstall an app which had previously registered as the handler for a file type it can remove the registry information and unwittingly un-register a newer app. ie. Install JMP 19 and then uninstall, say, JMP 17, the JMP 17 uninstall can remove JMP 19's registry information. The Reset Associations button is an attempt to help here but it does require administration privileges because of the portion of the registry it affects.
So, this is not a solution but perhaps an explanation of "what happened?" for people who may have run into this situation. The ideal sequence is to uninstall the old version before installing the new but obviously, that's not always possible.
And FWIW, a re-install ought to fix things up as well.