As I mentioned, intermittent operation is a clear sign of a connection issue somewhere, and it would be good to figure out the source of that bad connection since until we do, we cannot be confident that a replacement board will solve the problem. While it could be a bad solder connection on one of the SMT components on the board, that is unlikely as each board goes through automated optical inspection of all its solder joints followed by full functional testing, and a bad component connection wouldn’t explain why the Arduino’s VDD isn’t making it to the board. When you are pushing down, are you pressing on any specific component? Can you push in different places and still get it to work? If not, can you tell me which component you need to press on to get it to work?
If just generally pushing on the board itself (not just a specific component) gets it to work, then that strongly points to an issue with the connection between your Arduino and the board, not a problem inherent to the board itself, and some pictures might help us identify the issue. Could you post some pictures of the shield, both installed on the Arduino and by itself?
Lastly, can you use a multimeter to perform a continuity test between the VDD through-hole on the side of the driver that does not connect to the Arduino and the header pin that connects VDD to the Arduino’s VDD? Could you also check the continuity between a ground through-hole on the board and the header pin that connects ground to the Arduino’s ground?