Maybe you haven't connected auto reset (if your FTDI adapter supports it). Otherwise you have to manually reset your microcontroller when the IDE is finished compiling and started uploading, can be a bit tricky.
I'm using the Arduino USB2SERIAL LIGHT with a 100nF capasitor between EXT RESET on the adapter and pin 1 on my 328P for auto resetting. I have also a 10k pull up resistor from 5V to pin 1
Also make sure you have the RX and TX connected right. The RX on my adapter is connected to TX (pin 3) on the 328P and the TX on the adapter is connected to the RX (pin 2) on the 328P.