The Master System Glasses are an interesting concept for sure. They work well with a basic 3-D effect - when they do work. You cant take apart the glasses themselves (well, I am sure you can, but not sure I want to try). But you can take apart the card - and lucky for all of us, that is where the most common issue lives - the connector.
So how do you go about fixing them? Sometimes wiggling the connection will get them to work. But a better more long term fix is to take the screws out of the back of the card. Then carefully slide off the two plastic covers off of the card. Please note, always take care of PCB boards, and handle them only by the sides. Work in a static free environment. Dont blame us if something goes wrong.
The back of the card:
The bare card front side:
And the back side:
Front side of the card, there is the connection (like that from a pair of headphones) that has the issue. You can three silver wires there on this 'tube'. These are the pins that make contact with the plug. I took a small blade (flat head) screw driver and pushed in on the contact gently. Try to make sure your glasses can still plug in before putting it back together. You can also carefully give it a shot before putting the cover on it.
Once that is good to go, re-assemble the unit, and enjoy!