When teeth become sensitive I suppose it's because of enamel wearing away. Isn't this permanent? If so, then how come sensitive teeth eventually 'heal'?
What Causes Sensitive Teeth? - WebmD
Things that cause this usually break down your teeth so that other things reach your pulp or tooth root which cause pain when touched.
Tooth whitening products, etc
So it is wear, as explained here:
You get it when your gums pull back and expose the surface beneath, called the dentin. This soft layer has thousands of tiny tubes that lead to the tooth's nerve center (the pulp). They allow the hot, cold, or sweet food to reach the nerve in your tooth, which kicks off your pain.
While the above is just one scenario of how it can happen, the way your nerve reacts is not specific to that. Tooth sensitivity can be stopped by several methods depending on circumstance. Flouride can be used to help build the enamel of the tooth back, root canals can be used to eliminate problems in your root canal and are one of the most successful treatments for this. Also, there are grafts which cover the exposed root canal desensitizing root canal by applying resins. Using desensitizing toothpastes also help and preventing further wear of enamel is always on the treatment plan. The reason why sensitive teeth can get better is because the root canal is exposed and recovering enamel or desensitizing the nerve fixes the problem or makes it less sensitive to pain. While in this answer I may have used different terminology the word pulp, root canal and root are referring to the nerve in your teeth.