Hello Lorna, and welcome 🙂
Which insulins has your son got, and how many units is he injecting at the moment? And has he been given half-unit pens? - if not, I recommend your or he ask his diabetes team for some. A pump might also be an option (if he doesn't have one already) as it would allow him to have much smaller doses of insulin at a time.
I have insulin sensitivity too, and have hypos virtually every day, sometimes 2 or 3 a day - can't offer any advice as to how to avoid them, I'm afraid, but I can reassure you that I'm still here, six years after diagnosis. I tend to wake up if I have a bad hypo in the night and get an adrenalin rush which helps me get up and deal with it. I suspect I also get slight hypos in the night quite often which don't wake me up, but that my liver produces enough glucose to make sure I'm OK.
Hypos in the night usually result in splitting headaches in the morning, so that's a sign to watch out for, and a cue to lower basal insulin.