Electronic – D246A – what kind of diode is this

From the sounds of it, the diode model you are using is the simple "ideal diode" with a fixed forward voltage. This model is an open circuit when \$V_{\textrm{Anode}} - V_{\textrm{Cathode}} < V_D\$ (reverse biased), and a fixed \$V_D\$ voltage supply otherwise (forward biased).

Start by making assumptions about the state of D1 and D2 (for example, D1 is forward biased, and D2 is reverse biased).

Your circuit would then look like this:

^{simulate this circuit – Schematic created using CircuitLab}

What is \$V_o\$ here? The last step is to check your assumptions on each diode. If the assumptions are correct, the model is applicable. If not, permute your assumptions (ex.: what if D1 is reverse biased, and D2 is forward biased? or D1 and D2 are reverse biased, etc.) Only one of the 4 possible permutations will have a consistent answer.

As a side note, the answer you get will not match what the circuit simulator gives you (though it will be close). This is because the circuit simulator uses a more advanced diode model.

I suspect it has something to do with the initial forward voltage when you first apply power, which, because of the caps, will be the full supply voltage.

Although the S1D-13-F should be able to handle the full supply forward voltage and inrush current to the caps, "should" is the operative word here though.

You stated "I have had a few of these PCBs stop functioning" which suggests they were working for some time and then failed. That suggests something is getting stressed, and the peak forward voltage and current would be by prime suspect. If it IS overstressing it, then failure mode could be weird.

Moving the diode to the right of C1 would solve that issue. Easy enough rework to the cap connection too.. Though it does leave the cap open to being reversed, it at least limits the threat.

Ultimately, if it is a real and present danger of reverse connection, a better method is to use a different technique, such as a up diode between ground and 12V and a polyfuse. That method gets rid of that unnecessary diode voltage drop in the line too.

BTW. I would have wired that connector with the centre ground and 12V on both pins 1 and 3. That way it will not matter if it gets plugged in backwards.