160709-2403 EDT
larryv:
Your original post is not adequately clear and you need a good understanding of basic electrical theory.
I will make some asumptions as follow:
1. Your power source for the nominal 24 V to power the relays is an ordinary unregulated transformer with no output rectifier. Thus, the output is a 60 Hz AC, approximately, sine waveform.
This means the output terminal voltage is approximately Vin*K-(Zinternal*Iload). Vin is the input source voltage. This varies from moment to moment and has some longer term variation throughout a day, week, or year. K is related to the transformer turns ratio and can be considered constant. Zinternal is the transformer internal impedance as reflected and seen looking at the transformer from the secondary side. This can also be considered as constant. Iload is the secondary load current on the transformer.
Thus, terminal voltage is dependent upon on both the primary source voltage and the secondary load current. For a constant input voltage the output terminal voltage will drop approximately linearly as load current inreases.
2. Relays whether AC or DC have a higher pullin voltage than dropout voltage. But it is current that determines pullin and dropout.
3. The current to a DC relay coil is essentially constant for a given applied voltage independent of the relay state (position of the armature).
4. For an AC relay coil (one using a shaded pole, typical) for a fixed applied input voltage to the coil the current is quite dependent upon the armature position. Armature open and the current is higher than when closed. Thus, for a fixed input voltage to the coil there is initially a higher current until the relay armature closes.
In your application the steady state load on the power source may not exceed 500 mA, but if near the full load rating there may be a substantial voltage drop, many volts. Possibly down to 20 V from 25. That should not be a low enough voltage to prevent a nominal 24 V relay from pulling in.
But if the initial current for pullin is much greater than 500 mA, then the terminal voltage could be quite a bit lower. Combine this with a possible low input supply voltage and this could account for random pullin failures.
The pullin voltage could be higher for your bigger contactor than for the smaller ones and a reason for only the big one failing to pullin. If the big contactor does not pullin and power is maintained, then you could burnout the contactor coil and and/or the transformer secondary. The transformer may be self protecting by an internal thermal overload.
The precise pullin point for a relay is somewhat random over a small range. Line voltage variations are likely a greater reason for random pullin failures.
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