First, to recruit Pokémon there are some requirements you should make sure you don't miss.
The team leader must deal the finishing blow that causes the enemy to faint.
The enemy must be adjacent to the team leader when the finishing blow is delivered. However, Pokémon that are not immediately recruited when the final blow is dealt, but after a short cutscene (many Legendary Pokémon for instance), are an exception to this rule.
Some Pokémon, such as Omastar in Brine Cave are unrecruitable. In addition, many boss legendary Pokémon cannot be recruited on the first visit(Kyogre does not apply to this). In Rescue Team, all but nine fully-evolved Pokémon cannot be recruited and have to be acquired via evolving.
Now here are methods to increase the recruitment rate.
Have Pokémon of high level as your leader.
Here is the chart that shows the increased recruit rate:
Have a Pokémon with Fast Friend IQ
The IQ Skill "Fast Friend" raises the recruitment rate by 1%.
Have a recruitment rate raising item
These include the Friend Bow(10%), Amber Tear(24%) and the Golden Mask(24%). Here are also the seven treasures, but they only boost 10% and for a specific type.
These are all the ways to boost the recruitment rate in Pokémon EoS.
Hope I helped.