New cross sections for the rotational excitation of H+3 by electrons are calculated ab initio at low impact energies. The validity of the adiabatic-nuclei-rotation (ANR) approximation, combined with R-matrix wavefunctions, is assessed by comparison with rovibrational quantum defect theory calculations based on the treatment of Kokoouline and Greene (2003 Phys. Rev. A 68 012703). Pure ANR excitation cross sections are shown to be accurate down to threshold, except in the presence of large oscillating Rydberg resonances. These resonances occur for transitions with ΔJ = 1 and are caused by closed-channel effects. A simple analytic formula is derived for averaging the rotational probabilities over such resonances in a 3-channel problem. In accord with the Wigner law for an attractive Coulomb field, rotational excitation cross sections are shown to be large and finite at threshold, with a significant but moderate contribution from closed-channels.