My bad. That's exactly what the button on my router was doing as well. I can see that what I wrote gave the impression it was different. I've edited my first post.
I had this same issue where the power button wouldn't stay pressed in, not allowing my RT-AC88U to power on.
I bought a can of contact cleaner and opened the router up. I gave the power switch a decent spray (aka lots) and after letting it dry properly, the power switch now works as good as new.