I am going with Leakage, from the board documentation:
- The output control terminal must be connected to the circuit, and the working current must be> 50mA, so that the solid state relay can be disconnected normally
Unless your load current exceeds 50 mA you will get the described symptoms. The experiment with placing a lamp across the load demonstrates this. Rather than always having a lamp out there for each SSR a resistor can be used of enough wattage for each SCR output. Figure you have a 2.0 Amp SCR so you may want to place a 2.4 K resistor which will always be a 100 mA load.
Ron