How long does it typically take acid reflux to go away?

Varies. but in a great number of people it is life long. Frequently the reflux is associated with a medical (structureal) condition such as hiatal herna or motility issue such as with diabetes. These are not necessarily either temporary nor fixable.
Depends. Acid reflux tends to be a chronic recurrent problem. Each persons treatment varies on the frequency and severity of their symptoms. I do warn my patients to know the symptoms may not go away, or if they do that the symptoms may come back.
Acid reflux. It depends on the cause . Sometimes it goes away in 2 weeks if simple reflux responsive to antacids/PPI(omeprazole),antibiotics for H pylori or minor diet changes. Sometimes longer if associated with eosinophilic esophagitis, ulcers, Barretts esophagus ,celiac, complex food intolerences,smoking, high caffeine intake, spicy foods, fatty foods,high stress. See a doctor and discuss.