Balance is an interesting and complex thing. We get positional data from three main sources; prioreceptors in our body that sense pressure (for example in our feet, sensing pressure on the right side of our foot if we're leaning right), vestibular data from the balance organs in our ears, and from visual data on what's happening around us.
 My guess is that when our vestibular system is compromised from an AN or from AN treatment, one or more of the three vestibular data input sources is not working as before. The vestibular nerve on one side is often affected during AN growth, or even cut entirely during treatment.
 Many AN patients find that they can't visually track moving things as well, especially if a vestibular nerve is cut. It seems as if the patient's bandwidth to process "balance" data is reduced. For example, if things around the person are moving too much (people flying by in a crowd, or fast water moving in a brook), they can't process the visual positioning information fast enough, and may feel off balance.
 The brain is expecting the same vestibular balance data as before, ah, but things have changed.  Vestibular training therapy can involve trying to get the brain to affectively use the new balance data. For example, visual exercises to help retrain the brain to the new feedback it's getting from the eyes. Or exercises to help get the brain to perhaps weight one type of balance data over another compromised input. For example, an exercise where you stand in a corner (the walls are there to catch you if you begin to tip over), legs apart, then as that becomes easier legs together, then one foot in front of the other, then with eyes closed, then eyes closed while moving your head around. Somtimes this is all done while standing on a pillow, which is harder to do. All this is to retrain the brain to affectively deal with the modified balance input it's getting.
 If you have balance problems related to AN, I would really recommend seeing a Physical Therapist experienced in vestibular retraining. It can help.
Regards,
Rob