Why is this diode always off?
For negative Vin , current flows from ground to Vin through R2,D2 and R1.So there is a complete path for current to flow.

But for positive V1 , current can not go through D2 due to reverse biased condition  and there is no load at Vout. So there is no path for current to go to the ground. As a result, there is no current through R1 which leads to zero voltage drop across it. 

As voltage drop across diode D1 remain zero due to zero current through R1. But there is threshold voltage drop needed for diode to be ON, diode D1 remain OFF

In second image, there is a path fro current to flow through R2 is there in no reverse biased diode across it. So current flow thorough R1 &amp; R2  which cause voltage drop across R1. it created threshold voltage across D1 ,hence it's ON.