The rate coefficient for radiative and dielectronic recombination of beryllium-like magnesium ions was measured with high resolution at the Heidelberg heavy-ion storage ring TSR. In the electron-ion collision energy range 0-207 eV resonances due to 2s to 2p (ΔN=0) and 2s to 3l (ΔN=1) core excitations were detected. At low energies below 0.15 eV the recombination rate coefficient is dominated by strong resonances with the strongest one occuring at an energy of only 21 meV. These resonances decisively influence the recombination rate coefficient in a low temperature plasma. The experimentally derived dielectronic recombination rate coefficient ( systematical uncertainty) is compared with the recommendation by Mazzotta et al. (1998, A&AS, 133, 403) and the recent calculations by Gu (2003, ApJ, 590, 1131) and by Colgan et al. (2003, A&A, 412, 597). These results deviate from the experimental rate coefficient by 130%, 82% and 25%, respectively, at the temperature where the fractional abundance of is expected to peak in a photoionized plasma. At this temperature a theoretical uncertainty in the resonance positions of only 100 meV would translate into an uncertainty of the plasma rate coefficient of almost a factor 3. This finding emphasizes that an accurate theoretical calculation of the recombination rate coefficient from first principles is challenging.