This certainly sounds like a faulty button or connection.
Remove and refit the two wire terminals on the button as this will clean the terminals incase of any corrosion.
An ohm meter should be used to test the button.
If the button is faulty, replace it. If the button tests good, check the relay.
There is a section in the operators manual on how to trouble shoot the water resistant panels.
If you have lost your manual, you can download the complete operators manual from the factory website www.betamarine.co.uk