is your module randomly rebooting?
That's basically the result of a bad power source.
5v -> 3v3 might work, but will most certainly lead to the same result.
I am powering my modules using a cheap 12v/usb powersupply for breadboards, mine can be configured to either 5v or 3v3. It works like a charme and should cost only about 2$.
Note: You should connect the GND of your usb serial adaptor, so that you have a common ground.