RFID Reader Really Slow
I built a custom RFID card reader for the exact same protocol you are using and was able to read cards every time in just a few hundred milliseconds tops...

My reader included an Atmega328p connected to LC tank (large wire wound coil for L to act as antenna).. The LC tank was then reconnected to a pin of the Atmega through a 2 stage filter and then a schmitt trigger. 

I would say its a problem with the reader or something you are doing for sure... 125kHz tags are not that slow. Should be MUCH faster (as I stated, just a few hundred milliseconds tops, I never logged exact timing... but it appeared instantaneous to all users)