First, I assume that you are skilled in electrical work of this nature. If not, you need help from a proper professional or you might electrocute yourself or someone else.
I think your switch is the item S1.3 in the Optimum parts list. It contains a relay which allows the switch to hold itself on when electric power is applied, and which lets go (turns off) as soon as the supply is stopped. This can be by pressing the red button, or by any other fault in the supply, or you turning it off at the plug.
And it seems likely that there is a problem somewhere in which the relay does not hold firm – perhaps because
a) the on switch (the green button) has dirty contacts, or
b) because of a poor contact somewhere else in the supply.
If the problem is b) you will not cure the fault with a new switch only – you need to be sure that the other switches (including in the supply system) are in good condition.
The switch you show is very similar to the switches used in 'no-volt-release' switches common (in GB) on most workshop machines. I have one in front of me now, not exactly the same as the knobs are level and not sloping. But my guess is that the working parts are what you need.
If you look at e-bay you can try this address: **LINK**
Or just try 'no volt release' and look for a switch which matches yours as nearly as possible.
Make a careful note of which wire is connected to which tab, and check that any new switch has a similar wiring diagram to be sure of getting it right.
I hope this helps and that you can understand it all.
Regards, Tim