Traditionally, China's president holds three positions: President of China, Chairman of the Chinese Communist Party, and Chairman of the Central Military Commission. Long as that tradition continues, the PLA will continue to be directed by the CCP.
Economics is more important to China than anything at this point. The single greatest threat to PRC stability is the discontent of the middle class. The CCP has essentially made a deal with the populace since Deng's reforms: go along with the CCP and we'll let you become wealthy. If the CCP stops delivering on this (and the current downturn is threatening to end it), the party is going to crumble. A Chinese historian, Dr. David Aikman, said it this way: "I think China's leaders wake up every day and ask themselves, 'How are we going to hold this together for one more day?'" Dr. Ariel Roth described the situation like a treadmill: every day, China's leaders are running full tilt on a treadmill, worrying what might happen if they fall off.
Anything that threatens them economically also threatens their hold on the country.