MarkT:
Check your power supply is adequate and that neither servo is blocked from moving
by the mechanism - a stalled servo will heat up and cook itself quite quickly. Even small
servos need 1A or so each typically, and its a hugely common mistake to underprovide
the power for them.
I was about to suggest the same, a separate supply for the servos.. My general rule of thumb, 2 or more servos, NEVER power them from the on-board +5V regulator, ALWAYS add a 2ndary +5V circuit, a LM7805 regulator between the main supply (wired in parallel with the +9V power supply before the barrel socket, NEVER from the Vin pin) & the Arduino, to a supply rail for the servos...