What could be the reasons for the 4 wheel drive not to function on a Ford Explorer?

It would be helpful to know what year Explorer you are asking about, as there are different 4WD systems that vary by year. Also, if your vehicle is manual (lever shift), electronic "shift on the fly"(Push Buttons on the dash), or automatically goes into 4WD? Do you mean that the transfer case doesn't engage, or does the vehicle just not drive/handle like it should in 4X? If the transfer case is ingaging, but you're still not in 4X, it could be bad automatic front hubs. They do wear out and break if used a lot. Also check the Power Distribution Box / fuse panel, under the hood, Electric Shift is usually a 20A fuse. Sometimes the electronic solenoid on the transmission sticks, and the transfer case won't engage. This happens to Ex's that do not have 4WD used very often. Hope this helps.