Sending your child to boarding school is a very personal family decision and not one that is taken lightly. OP, ignore all these people slating you for doing what you feel is the right decision.
No experience of boarding myself but I do work at summer camps in the USA (yes I know, most people do this at university not in middle age!!!!). The kids attend for 7 weeks and are allowed just three phone calls home and one visit over the whole summer. The restriction on Home contact is designed to minimise homesickness and I must admit horrified me initially. But it works.
Most new campers have at least one wobble. Several have proper homesickness BUT it hits at the times they are not busy (mealtimes, bedtime etc). On the whole the rest of the time these children are beaming from ear to ear, genuinely happy and having an amazing time.
There are, however, one or two each year (out of 600) for whom it doesn’t ease. They are watched like hawks and trigger points observed and noted with a plan put in place to keep them busy. Parents are kept up to date twice a day. We give it two weeks and if there’s no improvement then they can have a call home. Sometimes they go home for a weekend which sometimes helps, sometimes doesn’t. Some children are just not cut out for it but it takes time to assess whether or not it’s something that can be overcome or whether they should return home and give it another bash in a year or two time.
I am surprised that in the circumstances your son is allowed so much contact without some sort of “support” from the school. If he is that homesick then why have you been left to contact them as opposed to them getting in touch with you?
Either he is not as homesick as he is making out OR hiding it extremely well OR these are issues with their pastoral care OR a combination of all of the above.
It honestly breaks my heart when I see 7 year olds in tears begging to go home but in the same day I have seen them spend ten hours having so much fun (genuine smiles, laughs and good times). I know it’s my job to work through it with them and they are the ones crying because they don’t want to leave at the end of summer.
I guess what I am saying is there doesn’t seem to be that great a team effort here to support your son. Get that in place, give it a couple of weeks and then reassess.
Start thinking about a plan B though. A couple of months of being miserable won’t scar him for life. A couple of years will. Be prepared for it not working but be mindful there are only a few children for whom it doesn’t work. Boarding today is a very different experience from days of Old.