The configuration-interaction (CI) method is applied to the study of positronic magnesium (e(+)Mg), positronic calcium (e(+)Ca), and positronic strontium (e(+)Sr). The CI expansion was seen to converge slowly with respect to L-max, the maximum angular momentum of any orbital used to construct the CI basis. Despite doing explicit calculations with L-max=10, extrapolation corrections to the binding energies for the L-max-->infinity limit were substantial in the case of e(+)Ca (25%) and e(+)Sr (50%). The extrapolated binding energies were 0.0162 hartree for e(+)Mg, 0.0165 hartree for e(+)Ca, and 0.0101 hartree for e(+)Sr. The static-dipole polarizabilities for the neutral parent atoms were computed as a by-product, giving 71.7a(0)(3), 162a(0)(3), and 204a(0)(3) for Mg, Ca, and Sr, respectively.