There will be a little play in the assembly. If there is too much play maybe the plunger and or coil stop has become worn/mushroomed.
The pop bumper can be thought of as 2 discrete assemblies. What is above the playfield and what is below. If the ball activates the pop bumper consistently via the skirt, but the downward action is sluggish, then you will want to tackle below the playfield.
Pop bumpers are not hard to rebuild at all, what makes them difficult in some games is their placement. It can require some contortion on your part to get at the right angle for repair.
If you want to rebuild to lower part of the pop bumper (which I highly recommend for maximum action, high speed needs nice fast pops!) you need to do the following.
Loosen and remove the 2 nuts that secure the metal ring to the plunger mechanism. There +SHOULD+ be washers behind the nuts so watch out for those as you are removing the nuts. Now with the nuts removed you'll see that the posts of the metal rod/ring fit into the holes of a metal and a Bakelite yoke. Make note of the positioning of the yokes and how they fit around the metal plunger in the coil. Pull the rod/ring assembly up and through the holes from the top of the playfield, while at the same time holding onto the yokes from underneath. (you will have to remove the pop bumper cap to do this). Inspect the rod/ring assembly for damage.
Many times faulty pop bumper action will be a result of a broken yoke, and most likely the metal one. I would order one of each to be on the safe side.
Now you can remove the coil stop. You shouldn't need to remove the coil bracket that attaches to the playfield or desolder the coil. You can let the coil hang there while you work.
Removing the coil will free the plunger return spring. This part needs to be replaced.
Inspect your plunger, if it has a rough edge on the end that contacts the coil stop then it needs to be replaced or you can file it down if its not too bad.
Inspect your coil stop. If it is not completely flat, or has a indented rough edge to it it should be replaced.
Clean and inspect the spoon and switch. The gap on this switch is important. You want it as close as possible so that the pop activates with glancing blows but not so close that vibrations make the pop fire.
Remove the coil sleeve from the coil and throw it away. Replace with a new fresh one. If you have a lot of resistance when removing the coil sleeve from the coil, your coil could have locked on at some point and may have been damaged.
Now just begin reassembly in the reverse order. It can take some dexterity to get the yokes back around the coil and the rod/ring reattached but its nothing horrible.
Once you see how quick and lively this rebuilt pop bumper is, you'll probably want to do all 3 so order enough parts in advance!
The top side is easy as well, but you will have to replace the lamp socket if you want to replace the skirt spring. I think your problem lies below the playfield so start there and if you want to do the top side, I can post those instructions later.
Good luck!