I have done similar work on a sewer cover (not much activity on it), an extension of a raised floor /step (2 inches deep, around 12 inches long, 3 or 4 inches high) into an outhouse for the boiler (again not much activity) - also something similar (step wise) into a shed - that does get activity... and is holding it's own.
You could try drilling into the surrounding concrete & putting thin steel spikes in, over hanging the area you are to concrete over... even some long nails /screws (drill the holes though, don't hammer as the force will just crack the surround) - just to give the new concrete something to hold onto.
Could be water eroding it, on top of general wear & tear...