I've been out of town for a week, so I didn't bother playing the iPhone 6s reservation system game all week. This morning, I dove in for a new round only to see that Apple's system still sucks. This morning I actually thought I reserved a device at Stanford only to be denied then returned to Stanford as an option for a second chance at reserving it -- which likewise failed.
My best guess is that Apple has some sort of widget or cross-site authentication working that my browser blocks (as I run a fairly locked down browser).
On a side note, while watching some television show or another, I happened to notice one of the characters using an iPhone and, probably because of the timing of when it was filmed, the older iOS interface was displayed on the device. It's an annoying reminder that, once upon a time, the iPhone used to be the best phone ever. And yet now, simply because of the user interface, I often find myself wanting to throw my iPhone across the room -- particularly after a number of repeated attempts to active some control that requires an extremely precise interaction with the touchscreen. That's the way that they've designed the new UI. Terrible.