I dusted off my Fire Wizard today, and played her for a bit. I was also watching tv :) So I was paying attention, but not 100%.
I cast two different fire spells (and started paying attention after I noticed this), and they are damage over time spells. The problem first - they would cast, but the little red thing that goes around the monster wasn't showing up.
It happened on the fire spell (sorry, don't know the names of the cards on these two :( ) that gives you health heal, and does 180 damage I think over 3 rounds to opponent. The second spell this was happening on was the one that does damage to all opponents (but not the level 48 spell, as I'm only level 45 on this wizard), I think it's 465 damage over 3 turns? It's 400 something damage.
However, when my fire minion cast the Fire Elf card after I cast one of the ones above, both fire damage things showed up on the opponent.
I believe the two spells you are referring to are Link and Scald respectively.
On-Topic
I too have noticed the 'disappearing DoT' (Damage over Time) symbols. I haven't thought much of it considering they come back anyways and still do the damage they're supposed to.
