Unstable for a variety of historical reasons..
Original primitive animist beliefs and Christian groups seem to have amalgamated in the first centuries CE.
The region was overcome by Islam coming from the Arab peninsula which then dominated its northern population centres and set up slave raid expeditions to the predominately animist / Christian south.
In the 1800s Egypt had taken control of the region and then Britain by virtue of their control over Egypt.
When Egypt rebelled and demanded independence from Britain in the 1950s the (soon to be) president demanded the same for the Sudan region as he was Sudanese. It's unclear if Sudan was remotely ready for this kind of independence the way Egypt was.
Discovery of oil and a predominantly conservative Islamic Arab northern population has caused Sudan to function like a gulf petro-state with about half of its economy being due to gold / oil extraction but very little of this helping the general population which remains in crushing poverty.
More extreme Islam since 1983 has seen academic independence suppressed (authors, poets imprisoned, islamic studies mandatory if studying anything etc).
Sudan's list of civil wars (Darfur etc) are generally characterised as animist / christian resistance movements against an oppressive islamic government. (Or, to take an opposite view, are wars of conquest by a disenfranchised rural population because in Sudan's petro economy, the controller of Khartoum is winner takes all)
Animist / Christian South Sudan finally managed independence in 2011. The peace apparently being bolstered by the economic coercion of gulf and Chinese corporations who seek a peaceful extraction of South Sudan's oil..
TL;DR blame Britain, or conservative Islam, depending on how long it's been since you were a student