Qatar doesn't need SA as much as SA needs them. They are somewhat close to the ocean and sea trade has been there for millennia. They have natural gas - which is in demand. They have still huge income to expense as far as tiny 300k population (native) is concerned. 

This whole affair is bad idea from the start for SA. They will be on the loosing end of the stick as they are facing the grim prospect of low oil. 

Oh, and what about Iran moving closer to SA - that must make them feel toasty.