Enhancements that are tossed are not being negated, they just aren't being played for their effect. It is not "essentially negating" them, it is more akin to restricting them from being played in their normal manner.
You stop toss by getting rid of the card that is forcing you to toss cards. Generally you'll do this by decreasing the tosser with toss or by using an out of battle card like writ or martyr to get rid of the card.