To help you catch suspects on foot, use Police Radio by FinKone, he included a tackle button you can press to pin them to the floor....
Also get Better Stun Gun, you can have one (if you choose) to have a stun gun with unlimited range, no damage, or full damage etc....which you can use to catch up to them, then try arresting them at gunpoint again.
https://www.gta5-mods.com/weapons/better-stun-gun
There you go, oh and if you play with a 360 controller - push the right analog stick down and press A about 3 times on Local :) (I think thats what you meant.) Press the stick down again to close it (you dont have to go down to cancel everytime.