Having had a season pass for years, my experience:
If you go the armband route, use it around your thigh, or even tighten it around your calf, just above your boot. I always had issues with the damn thing sliding off my arm. I don't like the resort supplied lanyards because they can break. That retractable cord isn't very strong at all. One tree branch in the woods, and you'll be waiting in the Season Ticket office for another pass.
Another good option is a small key ring looped through a zipper on your chest or waist and the hole in the pass (drill one if it doesn't have one already). Obviously get a beefier metal loop with a couple twists. Even a thick ziptie works well.
Or, if you're in the market for a new jacket, get one with an integrated pass window. Some have them on the sleeves, some on the chest area. Check out the Snow Expo when it comes to town in Oct/Nov. My Karbon jacket has one that comes out from underneath the left breast pocket. It's a plastic window, basically a plastic flap that can be tucked into it's own pocket, so it doesn't show when not skiing, like at the bars at night (K is known for the Pickle Barrel and Wobbly Barn apres-ski as I'm sure you know). It's got a magnet in the pass flap, and one in the jacket, so the thing doesn't swing around while skiing. I think lots of jackets now are showing up with these types of pass retainers.