Can I extend the life of a solenoid by reducing its supply voltage?
In general that is true, however you may find that the plunger gets crudded up with dirt and possibly magnetic particles during the life, so it fails to operate.
Also note that solenoids respond to current, not voltage, so if your coil is very hot (if it feels hot on the outside, the inner part of the winding is quite a bit higher in temperature) the current through the coil will drop substantially and it may not perform the desired function until it is allowed to cool. This can be exacerbated by high ambient temperature. That's because copper wire (most likely the wire in your solenoid) increases resistance by about +0.4%/°C.
If you want it to run cooler, you may be able to start with a higher voltage and then decrease the voltage after the solenoid has pulled in. The &quot;holding&quot; current is substantially less than the current to get the plunger to move initially, particularly if it is a type that closes the magnetic circuit.