Hi gschmelt..
To be honest after looking at the lousy documentation both these companies offer up as specifications I cannot come to any clear conclusion. (Sad)
Yaskawa's are especially poor including wrong/non functional diagrams.
So given the meager /missing information here is what I would do to hunt down the problem.
1) Does the signal across the outputs of your Phoenix change with the signal from the EYE?
IF NO, disconnect the relay's output hooked to the PLC's input. Hook a 4.7K (+/- 500ohms) resistor to the relay's output (you just disconnected) to the plus + of the power supply that is exciting your PLC's inputs.
Now check the voltage across the relay's outputs as you operate the EYE. If it stays high, 24V, you are not actually triggering the relay with the EYE or the relay is Kaput.
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IF YES, what do you read with your DC multimeter from the PLC screw across the relay to the supply ground? It must read more than 15Vdc in the OFF state (relay inactive)[reverse logic here] and it must read less than 5Vdc (relay active) to be considered ON.
Now if it never reads more 15VDC then disconnect the grounded side of your relay and see if the voltage on the other side(hooked to the PLC) jumps up above 15Vdc.
If the voltage across the relay changes as described above with the EYE being switched. But the voltage from the PLC input terminal to relay never gets above 15Vdc unless the the ground side of the relay is disconnected then indeed for whatever reason the relay has too much leakage.
You can often get around this by hooking a sufficient resistor from the +24Vdc supply to the PLC/relay connection to supply all necessary leakage current for the relay. Make sure if you use this method you calculate the resistor's power dissipation and make sure the resistor has a power rating of at least twice the expected dissipation. Otherwise you will have to switch the relay to a dry (mechanical) type contacts and they must be gold or mercury type.
Let me know what you find.