Is it possible for neck glands never to go back down after having chickenpox?

No, it is not possible for neck glands to never go back down after having chickenpox. The swelling of the lymph nodes in the neck is a common symptom of chickenpox, but it usually resolves within a few weeks after the rash has cleared. If the swelling does not go down within a few weeks, it is important to see a doctor to rule out any other underlying causes.