GFCI outlet tripping
I think Kenny above was right. 

From your wire count, on the load side, it looks like one black and one white go off to the properly-working GFCI outlets (which as others have pointed out need not be GFCI since they are downstream of a GFCI) while the "regular" outlets are probably getting a white from the GFCI load side, and a black from somewhere else (line side of the GFCI probably unless someone has accidentally mixed two circuits here).

This should be pretty easy to sort out and clean up, you just have to figure out which cable is the line feed, which goes to to downline kitchen outlets, and which goes to the downline regular outlets.