powered by the Arduino
Even small hobby servos can pull 1 amp each when encountering resistance. The Arduino 5V rail should really only power up to 500 mA. It may be that the power goes out and the Arduino resets when both servos get moving. Try powering them directly from a 6V power supply of some sort.
Also, reading the analog value twice, "once for each servo," seems unnecessary. The potentiometer won't have moved much between the first and the second reading, so you'll just get back the same value you got the first time, anyway.