"Probably hydraulics" is shorthand for "we have no idea" - which makes a mockery of the quoted £1600 - if they don't know the cause then they can't possibly know the likely cost - the cost of time while they make guesses.
What are you pressing? Having to keep pressing? A closure switch I suppose - that will probably "call" a relay (which latches on) and drives the hydraulic pump in the open direction - until a microswitch senses fully open - unlatches the relay and shuts off the hydraulic pump.
If the relay is failing to stay latched on then your continual pressing may be allowing the opening process by pulsing the open up relay.
If it were mine I would look for the open and close relays and swap them over - and see what happens.
I have no training, skills or experience in car roof opening systems (much like your garage I suppose) - I lack qualifications and have no confidence in my answer - but you did ask for ideas.
There will also very likely be a solenoid operated valve to change the direction of the open or close movement - you might look for it and see what it's doing in each direction.
Good luck...
Peccavi
August 2013