It totally depends on the seperation , the ∆ mag of the pair ( or more ) and seeing . The lower the ∆ mag , the lower the magnification required to split . Fine examples are Sirius and Izar .Also the lower the seperation , lower the magnification required to split . Albireo and Zeta UMa are good examples .
At last the seeing . You may have heard Sirius , Izar are sometimes impossible to split for some . Allan Wade in Australia has split Sirius with his TV-76 . Even Thomas Jensen split Sirius with magnification of ≈64 . But some reports say Sirius b impossible at 300×+ in 8"+ scopes . Why ? Seeing - you can have the best double star scope and eyepieces but if you don't have the seeing , you are going home 😉 . Also as Stu mentioned , collimation , cooling etc are also important .