While there isn't an explanation in Naruto for why a person is able to use Susanoo without his MS or Rinnegan, it has been done in the past.
The only logical conclusion is that after someone uses Susanoo, they can use it again without the Mangekyou Sharingan. The manga never explicitly stated that Susanoo required the usage of the MS. Rather it stated that Susanoo is the third technique MS users obtain after Tsukuyomi and Amaterasu.
When incorporating Japanese Mythology into the equation, we can reason that Susanoo does not require any eye techniques (and the below picture was not an accident). This is taken directly from the Susanoo Wikipedia Page:
All three were born from Izanagi, when he washed his face clean of the pollutants of Yomi, the underworld. Amaterasu was born when Izanagi washed out his left eye, Tsukuyomi was born from the washing of the right eye, and Susanoo from the washing of the nose.
Tsukuyomi and Amaterasu comes from the eyes, whereas Susanoo comes from the nose, so one does not need eyes to use Susanoo.
Source: Ch 577
Note: Itachi doesn't have MS activated. In the Chapter 578, Itachi activates MS when he needs to use it. Thus MS isn't required to use Susanoo. Also, when Madara fights the five Kages and has both Rinnegan, he is also able to use Susanoo.