How to wire latching SPDT relay using proximity switches without relay hanging
I wrote the original answer while feeling very ill and using EE.SE as a distraction. The answer was as garbled as my stomach and was inaccurate. I've deleted most of it and left what might be relevant.

Very often you need a little more understanding of what's inside a "black box" device especially if you want to use it in an unconventional manner as you are doing with the NC prox switch.







simulate this circuit &ndash; Schematic created using CircuitLab

Figure 1. The likely internals of your PNP switches. Note the protection diode D1.







simulate this circuit

Figure 2. The OP's schematic redrawn.


  [I] forgot to mention this but, it does work for a while with a new NC proxy then stops working. When it stops working the NC proxy doesn't break the current enough.


That was important information. It sounds as though the switches are being destroyed by inductive kick from somewhere. Add in the diodes D1, D2 and D3 below.







simulate this circuit

Figure 3. Protection diodes.




  Can you explain why diodes in that direction eliminates the induction kick?


When you change the current in an inductor a voltage is generated. This is shown by the formula
$$ V = L \frac {dI}{dt} $$
This is just saying that the voltage across an inductor is proportional to the rate of change of the current through it. If you change the current gradually you get a low induced voltage. If you switch it off in an instant then a very high voltage is generated. If you like, the inductor is doing this to try and generate enough voltage to keep the current going. You will often see this as a spark on a relay or switch.







simulate this circuit

Figure 4. (a) Switch closed, current flowing. (b) Switch opens, current continues to flow but high voltage is generated to cause the current to jump the gap. (c) Adding the snubber allows the current to circulate during switch-off. When the inductor / relay / solenoid is switched on the diode is reverse-biased and does not conduct.

Adding the diode allows the current to continue flowing but back through the diode. The current will decay to zero as the power is dissipated in the diode and in the inductor's resistance. The voltage across the coil is kept very low and so there is no sparking at the switch.

The snubber diode will delay the release of the relay or solenoid by a fraction of a second while the current decays.