Why would a runway friction measurement improve over time? Why would a runway friction measurement that I've just made (with a SARSYS friction tester) give better (condition improved) results than a measurement that I made 6 months ago? The runway has been in use in the interim and no repairs have been made in the interim.

The runway is asphalt and 15 years old. For both measurements, the runway was dry.
There could be a number of reasons. Temperature affects asphalt significantly or calibration could be off. 

But if higher friction is measured in the touchdown area after significant use I would look to rubber deposited by landing aircraft tires, which is stickier than asphalt. Dragsters do burnouts before their runs to put rubber on their lane. It is just like glue.