What appears to be happening is that the tire bead stretches and maybe tears internally, leading to it eventually being loose enough to pop off the rim. Heat from long descents and braking might be particularly taxing on the beads... but so far I've never heard of anyone having the tire blow off *during* a descent. It always happens randomly... many days after mounting, usually. Of course different tires have different beads, so they will respond differently. The 340s seem to be less tolerant than most other rims. They stretch the tire bead more and rely more on this tension to keep the tire on.
I'm no so sure about your theory about the tire bead stretching and tearing. Not just because Kevlar is very strong fiber, but also because tire retention does not depend on the circumferential strength of the bead - it relies on the strength of the 'clinch' between the bead and hooked rim sidewall. Even if the bead is completely broken, the clinch will keep the tire on the rim.
How do we know this? Two reasons. Firstly, here's an experiment that you can try yourself, involving purposely cutting a tire bead and installing the tire:http://sheldonbrown.com/rinard/tirebead.htm
I've repeated this test myself, only I cut each tire bead in 8 equally spaced locations. After mounting the tire, I inflated it to 140 psi and let it is sit overnight. The next morning, the tire was still on the rim. I then lowered the pressure to a normal riding pressure (100 psi) and went for a 30 mile, with several hard corners and quick stops. The tire stayed on the rim perfectly fine, even though the bead was severed in many places and had zero circumference strength.
The other reason we know that tire bead strength isn't required is from the observation of changes in spoke tension when inflating a tire. As many have reported, spoke tension decreases with tire pressure. This is because the tire is is squeezing the rim circumferentially, compressing the rim and relieving spoke tension. Bead tensile strength would be important if the tire pulled outward under pressure, but instead the pressure causes the tire to squeeze inward, making the circumferential tensile strength of the bead superfluous.
(So, one might be wondering how a tire can blow off a rim if pneumatic pressure causes it squeeze onto the rim harder. When a tire blows off a rim, it is not because the tire is pulled out off the rim radially, it is because the tension in the tire casing pulling in the lateral direction causes a portion of the bead to be slid laterally out of the rim. In other words, the pneumatic pressure causes the tire to want to become fatter, pulling the tire beads apart. Well, it would, except that the clinch between the bead and the rim sidewall locks the bead in place, preventing it from being pulled out.)
As for the Alpha 340 rim, I'm wondering if the problem isn't the internal geometry of the rim prevents the tire bead from seating under the hook properly, providing an insufficient 'clinch' to keep the tire on. Maybe the shape of the bead area of certain tires doesn't fit well with the Alpha 340's internal sidewall/hook geometry, making these tires more likely to blow off the rim.