From that image, which you say is from another project, the jumper settings indicate you are powering via USB. From what I can recall, a single USB port can source 500 mA of current, which I believe might be changeable in the BIOS (not sure, and 500mA is probably a max) .
Before I begin, this is all speculation because I have absolutely no idea what you are trying to do and how you are trying to do it. I have no idea of any of the specifications within the system, and so I will give you my first impressions I would think to check in my troubleshooting process.
Note: I am assuming that all of your programming and logic is sound, and functioning properly. If you are not sure, check your shit (especially from runaways/stack issues when your code is interrupted, that is, if you are using interrupts). If you are using a PWM register, there could be interrupt conflicts.
Again, since I know absolutely nothing about how you have it set up and what you are trying to do (aside from the general picture), my very first inclination would be to check the current draw of the servo motor and the RFID coil. If the peak current draw at any time goes over 500 mA (from the USB power) you could undergo a quick processor brownout which could flag an interrupt. This could hang your program if the USB voltage level sags or momentarily cuts off to prevent overcurrent damage. Again, I am not 100% sure about how the USB power supply is regulated, so I could be talking nonsense here.
Another possibility is that IF the impedance of the servo motor is much less than that of the RFID coil/system and draws all of the current from the supply, de-energizing the RFID system to a point that it cannot effectively operate.
If any of this is the problem, consider powering your servo from a separate power source (if not the whole system). However, in the world of small circuits, 500mA is a lot of current. However, I am not familiar with your servo's specs, and maybe it draws a stunning amount of current.
Is the servo rotor loaded? Maybe that is the problem? Check to see if the motor, processor, wires or RFID chips are unusually warm.
Without any more info I can only continue to speculate wildly like a jackass. If you can't find the problem, PM me with actual information and I can try to help you find the problem.