You know how it's very difficult to teach someone ballet dancing in their 40s? Same here. Especially for people with mixed parents, the majority. Your magical sensitive people have a period of time to learn magic otherwise their magical sense and ability becomes dull. 18 or 21 seems like a reasonable age. After that it's near impossible to teach them anything.
With a lack of will, teachers, or interest your people can safely ignore magic until they gradually become non magical.
Learning to ward "other" forces
Demons, evil mages or the like.
Your magically inclined group tend to...go away. Insanity from demonic voices in their head? Failing to summon a demon properly and have it rip the mage apart.
Being hunted to power spells. Committing suicide....
List goes on and on. Without proper guidance the very nature of magic or the world destroys them. Similar to the firs suggestion but different in that they are a ticking clock always in danger. Without the proper training.
Exhausting their magic
Certainly interesting to consider magic like currency. So. Your mages start with defined pool of magic. With usage it is used and does not recharge. You can have a couple of exceptions of course.
But normal mages have a limited pool. You can further limit this with training, how well they use utilize their magic for example. So. As they grow up and use more of it they just use it and can't be regained. Similarly they might still be technically capable of casting magic but with time they are down to a couple of spells.
Meaning in their every day life they are mages but will not use the very limited magic they have making them kinda normal in general.
Heck. You can complicate it further by adding a system where any magic casting costs the same amount of magic drawn from the pool and the mage's strength and will power, or whatever, determines if they can pull it off or not.
For example lighting a candle costs 1 mana point while burning the whole town also costs 1 mana point. But wait. Mage level 1 can only cast the first while a level 7 can cast both.
This might be interesting mechanic for a game in particular. For example your mages will tend to cast more powerful spells, if they can of course, in general as to ensure getting what they want since it costs the same anyway.
Governmental magic remove
Big comrade is watching you. Big comrade want you, yes you, to register in the mages lists to have your magical powers removed.
100 free. Available to all people. Pain free. And you get 1000 credit points.
Or whatever you configure to fit your world. Have it painless or painful. Brainwash people to actually want it or not. Whatever.
Result is the same. Government just "removes" magic from mages and viola they are fine.