The plaster flaking is known by plasterers as "spalling" or "delamination." The upper one-sixteenth inch surface is flaking off. The overall thickness of the spa floor is usually as least a half inch. The delamination is caused by improper troweling, usually adding too much water to the hardening surface too late in the process. Water chemistry has nothing to do with that occuring. The defects were there at the begining, a slight bonding problem, but not severe enough to flake off soon after filling. It usually take some time, temperature changes, or the draining and drying out will cause it to shrink and lose its bond.
It is very difficult to patch with cement, but power sanding may smooth out the rough edges and rough center areas. But that will be a lot of hard work.