What is the recommended power supply for use with the Arduino? 5vDC 1A? 9vDC 650mA?
At least 7V is needed to get past the linear regulator and get 5V out. The current depends upon what you are powering. The Arduino itself is likely going to be <50mA. You can use higher voltages (>7V) but then you just waste more power in the regulator.
So why would warm reboot (manually pressing reset on the Arduino) fix the issue?
There are LOTS of variables here, roughly broken up into "hardware" and "software". Without knowing what they are and how they interact, I can't speculate. Though I doubt it's a capacitor issue.
The Gadget Shield
: accelerometer, RGB LED, IR transmit/receive, light sensor, potentiometers, pushbuttons