In my experience, chronic abscesses have sometimes meant there's an unresolved underlying injury to the site of the abscess, perhaps coupled with a suppressed immune system due to Cushings or other such problems.
I would have an xray done of the affected feet. You may find bone infection, sometimes joint infection, or some other anomoly. If this is the case, I would pass on the horse unless he was already mine. These are expensive, labor intensive, long term issues to fix.
I would have the horse tested for Cushings Syndrome and other problems which suppress the immune system. Again, I would probably pass on the horse if he weren't mine, but if he were already mine, I would definitely treat the disorder and get his immune system going again!
If it is not a huge issue like this, I would recommend keeping the horse's feet as clean as possible and reasonably dry. Don't overdo it, though - too dry is as bad as too wet. If you bed on shavings, and you keep them completely dry, you'll dry out the hoof too much. Wet grass is not as big a problem as mud, because it's clean, but unless it dries out in the afternoons so his hooves can dry you may want to bring him in for a few hours so they can.
Do everything you can to prevent stone bruises and other hoof injuries that lead to abscesses. This means keep him on clean firm ground - not hard, not muddy, not rocky. Consider using pads under his shoes if he is shod.
If he can go unshod, great! The nail holes are an easy path for bacteria to enter and cause an abscess.
Keep his hooves correctly trimmed (and shod if necessary) at all times. No stretching out the times between farrier visits - a flared wall or cracked toe can let things start all over again.
Periodically check your paddocks and walkways for rocks and other things that can bruise the hoof, and remove them.
Treat any abscesses that appear correctly. Most veterinarians seem to recommend against using antibiotics on them unless there is swelling in the pastern above the ankle joint. It seems that these often suppress the infection enough for the horse to feel and look ok, but not enough to kill it off. The infection stays in there low level, brewing, only to erupt again bigger than ever.
So soak, poultice, and wrap the abscessed hoof until the abscess is clear, and for a few days after that to be sure. Then keep the horse on firm clean footing for a few days until the path of the abscess eruption has hardened up so no new infection can get in.
This is a significant issue.
Here's a link to some more tips that might help: https://www.usef.org/media/press-release...
Good Luck with him!