NFC tag affected by circuit board?
Antennas of NFC tags are typically made of coils with one or more windings. When current flows through the coil, it generates a field that goes through the center perpendicular to the coil surface.

If you put anything conductive (like a circuit board) behind or in front of that coil, it will prevent the magnetic field going through the coil. This reduces the reading distance of the  NFC tag. 

One thing that could help is a thin sheet of ferrite between the circuit board and the coil. This will restore the magnetic field to some amount. 

A larger NFC tag could help, but in most cases it will not, because larger coils have weaker magnetic fields.