Tough call, consider a few things here and we might get an answer.
(in these examples, assume that either the Parma or the Aegis was succesful in resisting a spell)
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If you cast a spell at a single target, the spell fails, its effect dissipated. It does not wait or hang in mid air as a trap for someone else to come along or for the original target to drop his guard later and then be affected. Such an effect would have to be specifically designed, and is not the case in the majority of spells. If it doesn't work at initial casting, the spell is gone. This is true whether it's cast at a parma or aegis.
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A spell or affect that was succesfuly cast on an object (Blade of the Virulent Flame) cannot pass through a Parma higher than its Penetration total. The spell was cast succesfully, but it still won't penetrate, and under a common ruling the spell and the sword under it would be deflected, but the spell, the flames, would not be extinguished.
If one were to try to bring such a sword with the spell on it into an aegis, the sword and spell likely wouldn't pass. Or would it, but extinguish the spell? This is the essential question. If it doesn't pass, that's simple enough; the spell and the thing it's attached to are blocked and can't cross the aegis. If the spell alone is resisted and the item/person/thing can pass, then what happens? Using example one, one would logically say that the spell dissipates, it wouldn't wait there (as if in midair) for the item/person/thing to return again and then burst again into life, even if it had the duration to do so. This is closely aligned the spell 'fizzling out'.
The other option might be is that the spell is suppressed, its effects completely diminished. A good way to look at that might be that the spell/item gets a bubble around it from the aegis and the magic cannot cross out of the bubble. The spell is alive, but ineffective. When the item/person/thing leaves the aegis, its bubble is gone and the spell comes back to life. This contrasts with the 'fizzle' effect. This also contrasts with the effects on parma, which to me is fine, the aegis is based off of, but different than parma. Game wise and visual wise though, this seems no different than the spell 'hovering in midair' outside the aegis and then reattaching when the item/person/thing returns. The difference is that it was always on the item but suppressed the whole time, but the overall affect is almost no different.
I like the suppressing idea, but I'd have to add a further caveat to it, as there are unintended consequences that can be taken advantage of. Someone with a magical curse could in theory walk into an aegis and be rid of it, if the magic of the curse would simply fizzle out. That provides a loop hole I don't care for. An alternative is that all aspects of the spell are suppressed, including the time that the spell/curse/effect lasts. So you have a spell on you that will last a Moon, you go into an aegis on day 1, wait for a Moon and walk out only to realize that the spell is still under effect as not a full moon has passed for the spell. To me that has kind of a magical/mythic flavor. Someone trying to avoid a curse might be able to do so, but is now effectively trapped within the aegis, and every time the aegis is recast has to suffer it for at least a little while.
These aren't answers, they're theories and suggestions at best, but maybe they'll help.