Why would a CFL bulb dim by itself after 60 seconds?
The Feb. 2012 issue of Consumer Reports had a sidebar about new hybrid halogen/CFL light bulbs as part of a review of light bulbs.  The sidebar includes a picture of a two-pack of GE Energy Smart 75W equivalent bulbs.  

These bulbs have a halogen bulb inside the CFL swirl.  The theory is that the halogen is used when the light is first turned on, providing instant light.  The waste heat from the halogen bulb helps to warm the CFL, allowing it to reach full brightness quicker.  The halogen is turned off after the CFL has warmed up, so you're getting the energy savings from the CFL from that point on.  The drop in brightness you're seeing is when the halogen turns off.

The CR review said that these bulbs didn't last well in a 2 minute on / 2 minute off rapid cycle test, but were otherwise very good to excellent.  It also pointed out that once the CFL fails, you'll have a bulb that lights for a minute, then turns out on its own.