New nuts and studs should be a good investment.
As to wheel loss it is more common than you'd think. As to why it happens look up Bolt Science. Basically there are two ways of fixing wheels to hubs. "Lugcentric" is where the weight is carried by the nuts and studs and "Hubcentric" where the wheel locates accurately on a centre spigot. Major car manufacturers now use Hubcentric as it is more secure. One disadvantage is that rusting can make the wheel exceedingly difficult to remove. As to the broken studs, overtightening is probably the culprit. Wheel nuts should be tightened manually preferably with a torque wrench, NOT hammered up as tight as the air wrench will go. As to the offside wheel coming off this is very unusual as precession (the reason why cycle pedals have opposite threads) will try to tighten the nuts on the right. On the left hand side precession tends to loosen the nuts. Trailers that use 3/8" UNF wheel studs can be rather problematic on the left hand side as when loaded to the limit the nuts can loosen. Threadlock will prevent this. Another way, if the studs are long enough, is the use of a locknut. I have in the past found broken HGV studs at the side of the road. Such studs are about an inch thick. Perhaps these components should be regarded as having a "lifespan" in a similar way to aircraft parts. Of course the problem could still be the slap-happy air-wrench-monkeys or potholes. At major car factories wheel nuts are robot tightened by computer. The computerised nut wrench actually plots a Hookes Law graph in its memory so to speak and the nuts are usually tightened up to the yield point. Not so easy to do in the field unfortunately but as the wheels are hubcentric they never fall off. Perhaps lugcentric needs to be relegated to the history books.
