Why do fluorescence intensities decline with replicate number?
That looks like a bleaching to me. The notion that bleaching only occurs with excesive light intesity on small populations of fluorophores is news to me. Might also that in my field we just use the bleaching term loosely. Best way to test is to take a long exposure of your sample and monitor the fluorescence intensity over time. 
With our chemistry we usually encounter intensity loss that can be fitted with exponential decay function which would explain the bottoming out that you are describing. We often take multiple such "bleaching curves" and fit them to correct for intesity loss in our experiments that can take multiple hours.
In case you are only exposing your sample for short periods i would just make sure you measure each sample the same number of times that should rule out any error between samples. Thus reducing to only one measurment will not make it more correct.
Bleaching is poorly understood thus far. There is not a way to predict what excatly happens with a specific molecule. 


Also how big is the effect for example (Start value)/(3rd measurment value) ?