If you're too Tough to die, do you still burn?
Whenever you are reduced to zero hit points, you are disabled.  Before you get boxed and removed from the table you have to resolve any effects triggered by being disabled(I.e. Tough).

So during your maintenance phase you roll to see if the fire goes out.  If it doesn't you take the POW 12 damage roll.  If this reduces you to zero hit points, then you are disabled.  Tough is triggered.  If you pass the tough test you are healed back to 1 hit point.  Since your model never left the table, Fire remains In effect.