It's not ignoring anything.
Take the following: a magic spell that grants the recipient +30 Strength for 1 hour. Don't worry about the construct except that it is bought as a Power (Characteristics bought as Powers are NOT Characteristics). The recipient of the spell is trucking right along, feeling great....and is hit with a Suppress, knocking that spell down to just +5 Strength for his remaining 45 minutes. Sadness occurs. Even more sadness occurs when he is then hit by a Dispel, eliminating the Strength bonus altogether.
But wait! That Suppress is going to fade. As soon as it does (and the total Strength exceeds the amount of Dispel), said spell snaps back into being on our intrepid hero.