There is an excellent instruction video on You Tube on winch solenoid issues. Your description suggests the solenoid is sticking. Go to You Tube WINCH MAX REMOTE PROGRAMMING. Exactly the same process and systems as Lewmaras used by commercial trucks. Also check the replacement price befor buying from Lewmar, I wanted a remote control for my anchor winch Lewmar £145 Winch max £35 exactly the same system.
I hope this helps