In article ,
says...

Start/Stop or On/OFF pushbutton switches are usually used with a separate
magnetic contactor. The start button (normally open) provides momentary
power to a holding coil. Once the coil pulls in, it stays energized via its
own auxiliary contact unless the (normally closed) stop button is pushed in.
Stop buttons are wired in series with the power to the coil so that any stop
button will drop out power to the coil. The older, self contained start/stop
controls that don't work with a contactor typically stay in when you push
them and don't have the safety features inherent in a start/stop circuit.


There are manual starters that include motor overload
protection. If the overload is tripped they will behave as
the OP described--the start button will not stay engaged
when pressed. It's not at all clear to me whether he has a
complete manual starting switch or just the start/stop
buttons for a magnetic starter. A photo would help.

Ned Simmons