Recommendation for low cost RFID receiver (approx 0.5 meter range)
The first problem you face is that the magnetic flux density will not be powerful enough to energize the passive tag at 500 mm. Power is transferred magnetically and it is flux density that dictates power transmitted to the tag.

Here is the formula that defines flux density at a distance Z from a coil that has a radius R: -



Here is a calculator that will give you figures for B\$_Z\$. 


If R = 50mm and Z = 0, for 1A in the coil, flux density B\$_Z\$ = 0.0000126 teslas. 
If Z increased to 50mm, B\$_Z\$ drops to 0.0000044 teslas
If z were 500m. B\$_Z\$ drops to 1.24e-8 teslas


It can be seen that the flux density reduces by over 1000 when distance increases from 0 to 500 mm. At a distance of 50 mm the flux has only fallen by about 2.9 times.

I think the only option you have is to redesign the coil to be bigger and increase the current into the coil. A 10 amp coil that is 500 mm radius produces a flux density of 0.0000044 teslas at 500 mm (same as smaller coil with tag at 50 mm) - this would be my starting point but you also have another really significant problem to overcome....

Powering the tag can be overcome with a bigger coil and more amps but think about what happens on a normal passive tag situation - the tag responds by modulating the magnetic field it receives and this is picked up by the reader. Now, with a distance of 500 mm, that miniscule modulation has to be received over that immense distance AND it has to fight the 10 amps in the reader's coil in order to register a return signal at the reader.

I'm not going to say it can't be done (because it can) but you need a really big transmit coil and some very clever electronics to discriminate a very weak signal in the presense of a very powerful signal.

One alternative is to find tags that transmit their ID using (maybe) 433MHz i.e. keep the data transmission "away" from the power transmission spectrally.