Recent experiments on electronic excitation of molecules by positron impact have shown much larger cross sections than in the electron scattering case. The challenge of understanding the origin of this enhancement, especially just above electronic excitation thresholds, motivates the search of theoretical explanations of the phenomenon as well as new experimental efforts to confirm the data. In an earlier theoretical effort, an application of the Schwinger multichannel method at two-state level of approximation for the X (1)Sigma(+)(g)-> B (1)Sigma(+)(u) electronic excitation of the H-2 molecule, gave cross sections with smaller magnitude but reasonable qualitative agreement with the experimental data. The purpose of this work was to study the numerical stability of the previous calculation and to investigate the influence of open channels (energetically accessible electronic states-multichannel effects) and closed channels (energetically inaccessible electronic states-polarization effects) on this transition. Our results show minor multichannel effects and a significative enhancement of the X (1)Sigma(+)(g)-> B (1)Sigma(+)(u) cross section at the threshold due to polarization effects if compared to the usual static results.744