Bullet-resistant tires works differently from vehicle armor, Vehicle armor simply increases your vehicle HP to 2000, but the default HP is still 1000.
Bullet-resistant makes your default tire health 15 instead of 5, get my point?
It does not temporarily set it to 15 hp but the default hp is 5, it makes the tire normal health 15 until your vehicle is destroyed, so if it was shot and tire HP lowered (you can check /tirehealth), just repairing the vehicle (with bodywork, not just the engine) will fix it and restore it to it's normal HP which is 15 if normal bullet-resistant tires and 30 if super bullet-resistant tires, you dont need to buy bullet-resistant tires again as you already have them on your vehicle but they are damaged and need to be repaired.