In some of the phones that I have repaired I have noticed that the small "cage" doesn't hold the micro sdcard snugly enough. What I did to "repair" this was apply a couple of layers of scotch tape to the back (the side without the contacts) of the micro sd card and trim it to the edges of the card and then slide it into the cage. This causes more pressure to be applied between the contacts on the card and the pins in the phone. Give it a go, it can't hurt. Start with one layer of tape first though.
Two things can cause the issue it's either software or hardware if you would like you can preform a master reset on the device to rule out software, you can find the steps here
If you are not familiar with a Master Reset please pay close attention to step one as it will link you to a doc you can look at so you do not lose any important information.
If that does not fix it and you have Premium Handset Protection you can still get the device replaced.
Although I cannot speak to Mikewithe's solution very much what I will say is if you give it a shot be very careful that memory card door can be very fragile.
The problem is resolved. It never would read the original card again although it works in my computer. I bought a new 32GB class 10 PNY microSD card. The phone drops it after an hour or two just like it did the original one. I went in to the T-Mobile store and found out I had the phone insured. Good thing too. Got the replacement phone the very next day. It won't read the original card but the new card works wonderfully. I have to think that there were bad contacts in the old phone that caused the card to go bad in a way that it would no longer work in the phone. Yet again, the card works fine in the computer with a USB adapter. Insurance saved the day. Thanks for the replies.