Solved by purchasing a better USB cable to connect the Raspberry Pi 3 to the power adapter. Apparently the previous one was giving a big voltage drop.
If you step on the same problem, ensure you usehave a quality USB cable for theproper power supply. The one I was using was a common 28AWG (size standard), the new one is a 20AWG (much thicker)official Raspberry 2.5A adapter works perfectly with me so far. Also, ensure that the red led on your Raspberry Pi is always ON. In my case it wasn't before, but I found out it signals that the input voltage is correct. So if it's not, your Raspberry Pi might not be fed properly.
If you don't like the official power, try using a better quality USB cable for feeding the pi: before buying the official adapter I switched from a common 28AWG (standard size), to a 20AWG (much thicker) and the HD was working. However I had occasional freezes, which disappeared after switching to the official power supply.