It was more complicated then that. It starts with basically understanding who the Mande people were. Mande actually means Manden people. Manden means Mali. Mali is either an Arab or a Fulani word for Manden.
Ghana, Mali and Songhay are all Manden empires. They all basically split due to internal strife and fighting internally among the Mande. Songhay was a vassal State that had to pay tribute to the Mansa of Mali. As time passed by Songhay sought independence from Mali. Mali's Mansas basically ignored the situation, but eventually Songhay gained strength and it's eventual independence when many influential Mandingos sided with the Songhay people after many Mandingos had a falling out with the Mansas. That is how Songhay got its start. It is more complicated than that, but it is important to note that many of Songhay's earliest rulers were Mandingos, which is why historians always point out that the Mande people empires in the Sahel were Ghana, Mali and Songhay. They always mention all 3 together, because they were all basically successor empires even though Ghana existed during the time of Mali and Mali existed during the time of Songhay. All of the Kingdoms were interconnected and the elites and leaders of all of those Kingdoms were Mande people.
To answer your question: no Mali was not strong enough to fight off Songhay, because many of Mali's elite citizens were now the leaders in Songhay and their armies were able to drive the Mansas armies out of the northern part of the empire. So the Mansas and the other Mandingos that remained in Mali had to shift their focus to attacking lands to their south and to their west, which we now know as the Mane Invasion. The kicker is that that the Europeans had arrived on the west African coast at around the same time as the Mali/Songhay split and the Europeans actually recorded the invasion of the Mane/Mande/Mandingo/Manneh. It is very complicated and also very interesting.
