I've used solid stain on a white picket fence that has held up very well (I recoated it after 6 or 7 years). I used solid stain to prevent what has happened to you. I was told the stain would fade, but not peel--and that was my experience of it. (I used the ACE brand of solid stain.)

I don't have any snow, though, just really hot weather (I'm in California).

He should have used an oil based slow drying primer. The problem with fences though is that the end grain (the rough part that faces the ground) is almost touching the ground and never gets painted or sealed. All the moisture enters there (rain and snow). It's really like a sponge at the bottom of each piece of wood. So, even when primed and stained properly, you will probably still have peeling problems at the bottom of each board every two years. If you can get under each board and prime that end grain, that will help. Do not use a paint though. Paint will surely peel quicker than stain. Paint forms a film and stain breathes. Stick with the stain.

Maybe this is why my fence has held up so well. I did use an oil based primer before applying a latex stain. And I was able to prime and stain the bottom edges of the pickets because I did it before the fence was built.