Is there a prohibition from the Prophet, peace and blessings be upon him, against facing away from the Qibla in the mosque?

There is no hadith prohibiting facing away from the Qibla in the mosque. Rather, the evidence indicates the permissibility of facing away from the Kaaba in a gathering. It is narrated in Sahih Muslim that Ibrahim (peace be upon him) was "leaning his back against the Frequented House (Al-Bayt Al-Ma'mur)." Al-Nawawi cited Al-Qadi's statement that this indicates the permissibility of leaning against the Qibla and turning one's back towards it.