This is just a quick and dirty hack that i have had to perform once in a while. Sometimes and I have to say this problem is quite rare the catch that holds the microSD card in the socket fails and it is impossible to get the card to stay in place.
I have had this problem passed over my desk a few times I have a little fix/break for this that works.
WARNING: ONLY TRY THIS AFTER EXHAUSTING ALL OTHER POSSIBILITIES OF REPLACEMENT OR REPAIR AS YOU WILL BE DAMAGING THE MIRCO SD CARD SOCKET FOR THIS TO WORK. THERE IS NO GUARANTEE THIS WILL NOT RENDER YOUR RASPBERRY PI MORE BROKEN THAN IT ALREADY WAS :) I TAKE NO RESPONSIBILITY FOR BROKEN RASPBERRY PIs
So basically we are going to remove the catch and spring that retains and ejects the SD card. Hopefully without damaging the contacts.
Once that is lifted then used the tweezers to hook out the the plastic catch and spring.
Then it is just a case of folding the tab back down again and squeezing the housing slightly so that it applies some pressure on the SD Card when it is inserted.
After that it should be a case of sliding in the SD card and powering up if you have done this right the Pi should boot.
I normally add a little tape over then in SD card just to make sure it don't knock it out.
Hope this helps some people out as mentioned at the beginning you are essential breaking the socket to fix it.