I am working on a Cars themed animated project. I watched a tutorial on how to make wheels spin based on the movement of the character. In the tutorial it works perfectly, but for me the wheels spin only for 4 seconds and then they stop spinning, is there any fix to this ?
Hi! Welcome to the forum 
Without the blender file it is a bit hard to tell! Could you maybe share it?
Something I can already say from the screenshot is that your driver doesn’t reference any bone of the armature!
Also: You used Quaternion rotation for your wheel. Quaternion Rotations work in a bit other way. The XYZ and W Values influence each other. And when only one of them is getting changed without W or the others changing as well, it won’t work.
Quaternion is usually being used to avoid a “Gimbal Lock” happening for objects/bones that can rotate in every direction. But since wheels can only rotate onto one Axis, using Quaternion Rotations is a bit overkill
Change the Rotation Mode to XYZ EULER and try it with this