I believe the issue right now is that, while the Kleins have appealed the ruling, the popinjay jobsworth who is persecuting them ordered that they have to pay it now, and sue for the money back should they win on appeal (which is very unlikely, now that the clock has run out on the SCOTUS and Obamacare cases forcing Christians to violate their beliefs).
I don’t care if their appeal is frivolous (and most litigation is frivolous), they should file appeal after appeal on having to hand over their money to the thugs, until everyone involved dies of old age.