Well, I just ran the sim again and sure enough shorting or reversing D4 causes symptoms pretty close to what the OP is experiencing.

I just ran both D4 in reverse and with a short in its place on my breadboard setup, and not only did Delay 2 not produce an output, neither did Timer 1! So unless there's a damaged 555, I think we've nailed the problem!

 

I can't take any credit.