You need to remove the pickup from the mounting ring or pickguard. Sometimes the plastic in the pickguards can shrink, making it difficult to raise or lower a pickup. Many times the height adjust springs are too long for a particular position. You can reduce the length of a spring or rubber grommet that will allow the pickup to be adjusted higher.
A more complicated situation is when the neck angle is not correct and permanently set. A qualified repairman needs to make a special mounting ring so the pickup can be adjusted higher or reset the neck angle. If the pickup is adjusted to it's maximum height on a Fender style instrument, check the neck angle and perhaps the neck is not tightened properly or a shim has been added at the end of the neck between the neck and neck cavity. Again have a qualified repairman look at it. It can save you time and money.