Writing as a barefoot trimming specialist with over 12 years of experience, your horse’s recurring abscess problems are almost certainly due to contracted hooves and/or metabolic problems/sudden diet changes. My advice is to find the best barefoot trimmer in your area and work with them to improve your horse’s hoof quality (you might want to check the Trimmers List at http://www.thehorseshoof.com). Rehab should include providing your horse lots of turnout time (24/7 is optimal) in the company of other horses. Moisture (daily exposure of water up to the level of the coronary band), hoof Mechanism (physiologically correct hoof shape allows reversible expansion and enables vital blood circulation) and Movement (on firm, level, non-concussive terrain) all play critical roles to achieving permanent improvement.
Abscesses usually form in hooves from chronic pressure that cuts off blood supply, causing localized tissue death (basically too much horn in too small a space, = contraction). If the necrotic area is too large to be removed by blood circulation, an abscess is formed (rarely is an infection involved). When solar abscesses are involved, IME there is often a weakness/stretching in the laminar connection, causing the coffin bone to drop downward in the hoof capsule. This puts painful pressure along the lower surface/edges of the coffin bone where it is not designed to carry weight. In a reasonably healthy horse, these problems can nearly always be corrected by a correct barefoot trim and more natural equine lifestyle. Please keep in mind it takes about 8 months to fully replace a hoof growing at a normal, healthy rate so that considerable patience and dedication may be required in some cases.
Since you also described your horse as a hard keeper, you might want to have him evaluated for Cushing’s (PPID), which would predispose him to laminitis and thus solar abscessing. SmartPak makes a Pituitary Support supplement that is absolutely incredible! In the meantime, I’m also a fan of Soft-Ride boots (not really designed for riding but excellent during rehab). And extremely important–immediately get your horse off all sweet feeds or anything else high in NSC (simple sugars such as molasses) which will definitely cause or exacerbate laminitis (and hence solar abscessing). Good luck and hope you keep us updated on your progress!