Sounds like what happened to mine, clip broke off the wee runner mech..
I got a replacement from a scrapyard out of some sort of Audi (a lot of VAG cars use the same card holder), cost about £10squid. Take the two screws out below the radio fascia and gently pull the whole front away from the dash, i.e. the whole front fascia covering the radio, heater controls, card holder, etc.
Then just give the card holder a real good YANK and it should come out. I just slotted my new one in and it clicked into place. Refitted fascia and good as new