Why does the drop rate drop after the first time you defeat a act boss such as diablo. and is there a way to increase the amount of drops gained?
You are guaranteed a rare drop from all bosses on your first time killing each boss on normal difficulty. As of the 1.05 patch, you get "improved loot" for the first kill of a boss on every difficulty (its not clear exactly what this equates to yet). The intention isn't to allow players to farm, but to allow them to acquire enough gear to survive going forward.
After your first time on each boss, the only way to increase drop rate is through magic find and the Nephalem Valor buff