If on-site slump test fails, should engineers allow the contractor to continue the concreting work?

it depends on the failure ........if the concrete is bleeding and segregated ...then NO it must not be allowed ...but if the concrete carries lower than the specified slump , admixtures on site can be added .................plastic slump varies much now a days as3rd generation SP,s are used ...so you have to read alot about it ....hope my answer is helpful a little .....Thanks