Howto use/shield NFC/RFID Sticker on back of iPhone 5?
There could be at least a couple of reasons the MiFare card is not being read:


The reader is receiving too much random electromagnetic signal from the phone itself, drowning out the RFID sticker's response
The RFID sticker is not receiving a suitable RF ID request signal from the reader due to signal interference from within the phone.


For the first, there is not much one can do: If the mobile generates enough RF in the RFID device's frequency range, it will flood out any other RF communication in its vicinity.

For the second, try taping the MiFare sticker to the inside back of the cellphone case with conductive copper tape:

 (source)

Ensure the entire phone-facing side of the MiFare device is covered with the copper tape. This will work as a "Faraday cage", blocking RF in both directions, between the sticker and the phone. 

Given that small rolls of copper tape are sold for a couple of dollars or less, this is an inexpensive experiment to try.

Keep in mind that the signal reception of your mobile may reduce, in specific situations, because you are also blocking a part of the regular cellular signal reaching the cellphone's antenna.