If the card that you own has the ability that follows, Stop: x, where "x" represents any ability such as "Power +2", then the ability only activates when a card with the ability "Stop Opp. Ability" goes against it. That's how "Stop:" cards work. If the card that you own doesn't have the "Stop: x" ability, then post a screenshot of the glitch as it is occurring, or name of the card you are having a problem with so we could help you out some more.
Is it a Stop: ability? Or a Stop Opponent's Ability?
Like Buttacup said, if you have a card like Ashiko who is Stop: +3 life, it means for Ashiko to gain his ability he must go against a card like Bogdan who has soa, or a card from Roots / ghiest with with the bonus active. So a Stop: ability is only activated when that card verses a card with Soa.
IF that made no sense feel free to pm me xD
If the card has an addition to the Stop opp. Ability, you may not be using it right, Courage requires you to pick your card before the opponent. Lin Bee is one example, if you pick her, and then your opponent picks a card, you will have SoA, but if your opponent picks a card and then you pick Lin Bee, it'll be crossed out as if it was stopped.
Confidence requires you to win the previous round, Revenge requries you to lose the previous round, and Stop: requires you to go up against a card that has "Stop opp. Ability"
When you Stop a Stop: the Stop: will be Stopped which means that it will not actually be stopped but rather unstopped. If you have Stop Ability and you stop a Stop: ability then your Stop Ability Ability will not stop any ability at all.