Licking the air is often a compulsive behavior that helps dogs cope with anxiety, but it can also be a sign that a dog isn't feeling well. In either case, it is not a behavior that should be ignored.
According to the ASPCA, anxious dogs might use several different compulsive behaviors to soothe themselves. These compulsive behaviors include air licking, chomping at the air, spinning and pacing, generally in direct response to triggers that make the dog nervous. However, if a dog does not seem anxious, air licking may be a sign of physical illness. VetStreet lists several health concerns that share air licking as a common symptom. These problems range in severity from nausea and gastrointestinal discomfort to seizures. Dental pain is another common cause of air licking.
Even if a dog is simply licking the air to relieve anxiety, a dog who cannot calm down without engaging in compulsive behaviors should be brought to a veterinarian for an evaluation. In some cases, a seemingly harmless compulsive behavior like air licking can escalate into self-destructive habits that may lead to injury. While some anxious dogs might need more exercise and a better diet, others require medication to help them lead normal lives.