From what I can see, your wiring looks OK.
So I just wired up 3 "channels". Each channel (I'll call them A,B,C) is a diode (1N4003) followed by the capacitor (1uF)-resistor (1M) pair going into the FRM01 CH1 trigger terminal. FRM01 is set to Mode --02 as your photo indicates. I set the T1 delay to 4 seconds.
I applied 12V to A. FRM01 relay clicks on for 4 seconds. After relay clicks off, I applied 12V to B (with A still "on") and FRM01 re-triggers for another 4 seconds. After relay clicks off, I then applied 12V to C (with A and B still "on") and FRM01 re-triggers for another 4 seconds.
I also tried it with the power supply set to 10V DC and 14V DC to rule out any voltage sensitivity in case your 12V supply is not exactly 12V. Same result.
But I hear what you're saying - you're seeing the circuit fail to perform when just 1 channel is already "on". I'm not sure what to suggest!
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Just to be clear, this simple circuit does have its limitations. After maybe 5 channels already "on", additional channels may not re-trigger the FRM01. I didn't think this would be a practical requirement - though handling an arbitrarily large number of "on" channels can certainly be done with more parts. While I can't imagine why this would be different, confirm the two resistors on the FRM01 next to the CH1 trigger input screw-terminal are as shown - marked 203 and 103 as shown (that means 20K and 10K Ohms respectively).