I'd say the air pressure between the door and the storm door does not let it close (the most common cause) but you're saying it does that with no glass in it (or with screen instead) too? Then it's definitely a mechanical issue.
Is the striker hitting the jamb before the striker plate by chance? By now you'd see the spot all blackened by graphite if it were. It it's anything other than metal of the plate, it will create unwanted additional friction. The plate itself may have a sharp edge that will try to grab on the striker - perhaps it needs to be filed off or bent lightly to make the striker come in at a more shallow angle.
Perhaps you can adjust the air pressure in the cylinder - unscrew the control screw a little to let it close faster so the inertia overcomes the friction in the striker. Or, if that makes it close dangerously fast, see if you can re-attach the mounting bracket as far away from the storm door as the jamb allows to make the closer push at a less acute angle which will create more torque.
Which closer, BTW? Some are better than others, so instead of pulling your hair out might be a good time to just get a stronger closer... Also, if I were desperate, I might have tried to grind the striker so it comes in at a more acute angle to the plate. Some fine grit polishing will be needed after that though.
- posted 7 years ago