Big Show will continue to put on a show that includes rope climbing ... sources connected with the WWE tell TMZ.

John Cena averted serious injury during a match in Manila Friday when the rope on which Big Show was standing snapped, sending him tumbling to the mat. Cena rolled to avoid impact.

We contacted WWE sources to find out if Big Show will continue standing on the ring ropes. If his 440 pound weight was simply too much, the WWE could face serious liability if it happened again and someone were injured.

We're told the accident was "a fluke" and the rope was simply defective. Our sources say the ropes are Big Show-worthy and the wrestler will go into the ring in future matches undeterred.