Since the bootloader of the Arduino Nano has been updated, we recommend you to update the cores for the Arduino Nano board following the steps below and let us know if then you can successfully upload the sketches:

• Go to Arduino IDE > Tools > Board > Boards Manager
• Look for "Arduino AVR Boards", select the last version (1.6.21) and click on "Update".
• Then, before uploading the sketch make sure you select the proper board (Arduino Nano), processor (ATmega328P) and port (the one where your board appears) on Arduino IDE > Tools.

In case it still does not work, please let us know the following additional information so we can look further for a solution:

• Operating system of the computer and version of the Arduino IDE. 
• Version of the Arduino AVR boards (screenshot of the Boards Manager of the Arduino IDE where we can see the AVR core).
• Did it work before? If so, which one was the last working sketch on the Arduino, circuit and power supply.
• Screenshot of the Device Manager of the computer (with “Ports” open) with the board connected if using Windows.
• Go to: Arduino IDE > File > Preferences > Show verbose output: Select both options: "Compilation" and "Upload". Then try to upload the Blink example (Arduino IDE > Files > Examples > Basics > Blink) and please send to us the copy of the whole text shown in the console.
• The invoice and one picture from each side of the board.