Computed lifetimes for the 3p $^{2}P_{1/2}$, P3${p}^{2}$${P}_{3/2}$, 3d $^{2}D_{3/2}$, and 3${d}^{2}$${D}_{5/2}$ levels in the sodium isoelectronic sequence are presented for Z=11--54, 74, 79, 90, and 92. These calculations agree well with recent high-precision lifetime measurements, and conflict with some ab initio estimates which indicated lifetimes shorter than those experimentally observed. Our calculations involve the inclusion of experimental energy-level data and the use of a realistic model potential, which utilizes comprehensive spectroscopic measurements that have recently become available. We also demonstrate that the core-polarization effects are significant and must be included to obtain agreement with experiment. As part of the study, we used the existing data base and Dirac-Fock methods to determine new values for ionization potentials in this sequence.