Did any of the Andalusian taifas have a sizeable chance for retaining independence?

Razgriz 2K9

Banned
After the collapse of the Umayyad Caliphate of Cordoba of 1031, its territory was divided into as many as almost 3 dozen petty Kingdoms known as Taifas, many of them weaker than the Christian Kingdoms to the North (in particular the Kingdoms of Castile and Leon, who combined conquered most of the Taifas between the 5 Christian Iberian Kingdoms), as well as the Moors/Moroccans to the South (the Almoravid, Almohad and possibly attempted but failed on part of the Marinids)

Was there any Taifas out there however that could've resisted the power of both states, even if going as far as conquering fellow Taifa Kingdoms, in order to preserve their independence for an extended period of time (say up to around the OTL Fall of Granada and beyond?)
 

Razgriz 2K9

Banned
The next question is, what steps could they achieve to retain independence from either the Catholic Kingdoms or the Moors?
 
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