Count me in the camp of "there are way too many independent variables and not enough opportunities for data collection to draw meaningful conclusions about performance degradation over time." The execption would likely be RAAM and guys spending 20+ hours on the bike for multiple days. There's a bunch of great data on the RAAM website and you could go play with that to see how speed changes over time.
But for randonneurs and the rest of us slow folks.... I think you'll find results are all over the map. On one 1200K I had no change in speed over time. But then I spent almost 24 hours at the overnight controls (that was a seriously fun 1200K!). On the same route 4 years earler, I was 20 hours faster in my finish time but my splits were 50% on Day 3 of what they had been on Day 1. I was very tired and I was injured.
But then I'm about as unscientific about this stuff as they come. Power Tap? Heck, I don't even use a cycle computer any more!