Can you access the secret level in Diablo 3 more than once per difficulty?

In the secret Cow level of Diablo 2, if you don't kill the Cow King, you can go back as many times as you want by creating the portal in a new game of that difficulty.

Can you access/farm the secret level in Diablo 3 more than once per difficulty?

According to the wiki at IGN, you can run the secret area as many times as you like. This has been confirmed several times since, including this video. Once you have a Staff of Herding for a difficulty, you can enter the secret area as many times as you want.

You can use the staff from a higher difficulty to open the secret level in a lower difficulty so you can feel free to create the Hellish or Infernal Staff of Herding when you're able.