Why does my Achilles tendon continue to hurt after jumping?

Potential injury. Pain is a symptom of injury which can run the spectrum from mild strain to full tear. A full tear is not the current concern since that would prevent even normal walking. You likely have an achilles tendinitis (inflammation). At worst an impending tear is present. Avoid further jumping until you can be evaluated by your physician or health care provider.
Have you seen anyone. If you are still having pain after jumping (you didn't specify in what activity) it is worth having a physician take a look at you. Sudden movements in particular certain jumping activities can predispose the tendon to injury or even worse rupture. Have a specialist perform a thorough examination.