Hello again,
Just wanted to update my post, in case someone here has been or is experiencing the same issue as me.
I have managed to solve this issue by letting the battery of my Bebook Neo comletely drain. Since it was impossible to totally turn it off, I turned off the automatic turn off after a certain time (not that this did any good, since it turned off after a little while regardless of the setting) and also turned on the wifi. I then let it be untill the bluie indicator light went dark, which means the battery is totally drained.
After waiting a while, I charged it and turned it on, navigated around, browsing my boks a little, in order to see whether it would turn off by itself again. It didn't. I went on turning it off, checking whether it would still stall leaving the indicator light shining. It did not. It was, and is behaving exactly as it should. Problem solved.
I attempted this solution, since remembering that the flatest firmware that was officially released to the e-reader had this bug that never got fixed by the company. The bug is that if the battery indicator falls below the third line (in the battery symbol (at the middle of it)) some problem may occur and the Neo may start acting weirdly.
Hope this may help other booklovers in this forum.
Take care, and happy reading everyone!
/T