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Have a Pokemon with the move called Mean Look, which Golbat is a primary choice to have this move. The move Mean Look prevents the Pokemon from fleeing or switching out during a battle and can be very useful in a battle like this. You cannot stop Mesprit from permanently fleeing, however. It is recommended to bring a Pokemon with any sleep status moves like: Hypnosis, Sleep Powder, Yawn, etc. to further the effect.
You could just use pokesav?
No, Scary Face is not a trapping move - it only decreases a Pokemon's speed, so it won't prevent Suicune from fleeing.
Mean Look is effective against the Pokemon Mesprit to prevent it from running away. Keep in mind that Mean Look ends when the Pokemon that used it is switched out or faints.
It will keep fleeing unless you have a Pokemon with Mean Look or something like that so it won't escape. Try catching a wild Golbat. The same is for Mespirit.