You can check if the reset signal is changing when you press the reset button by using a multimeter to test the voltage at the reset pin (pin 1 of the IC) - top left corner near the notch. Measure the voltage between it and ground. It should be at 5V normally going to 0V when the button is depressed.
That would at least tell you if the switch is working or not.
One fault that would probably lead to the symptoms you have (i.e. no automatic reset when programming) is the switch failing to a short.
A better compromise than the really cheap boards from China are the named closes like the Roboduino and Freeduino. I have a few of these and have not had any trouble with them.