Bare Kevlar does degrade significantly when exposed to UV. As dbeeksci pointed out in a different thread, high performance racing sails are often made of Kevlar. Sailmakers try to protect it in various ways, like with mylar skins and various UV coatings, but I've read that once a Kevlar sail is "sunburned" and turns from gold to brown, it has lost about a half of its original strength. Then again, Kevlar starts out about 5 times stronger than a Dacron sail, so it's still going to be strong. I'm not sure if UV degradation actually makes Kevlar more likely to fail catastrophically (e.g. brittle and snap) or if it just not as strong as original.

That said, I'm not sure if this sailcloth info has much bearing on using Kevlar thread as a paracord replacement in a survival situation, though, so YMMV.