The dilepton transverse momentum spectra and invariant mass spectra for low pT < 0.15 GeV/c in Au+Au collisions of different centralities at √ sNN = 200 GeV are studied within the partonhadron-string dynamics (PHSD) transport approach. The PHSD describes the whole evolution of the system on a microscopic basis, incorporates hadronic and partonic degrees-of-freedom, the dynamical hadronization of partons and hadronic rescattering. For dilepton production in p+p, p+A and A+A reactions the PHSD incorporates the leading hadronic and partonic channels (also for heavy flavors) and includes in-medium effects such as a broadening of the vector meson spectral functions in hadronic matter and a modification of initial heavy-flavor correlations by interactions with the partonic and hadronic medium. The transport calculations reproduce well the momentum integrated invariant mass spectra from the STAR Collaboration for minimum bias Au+Au collisions at √ sNN = 200 GeV, while the description of the STAR data -when gating on low pT < 0.15 GeV/c -is getting worse when going from central to peripheral collisions. An analysis of the transverse momentum spectra shows that the data for peripheral (60-80%) collisions are well reproduced for pT > 0.2 GeV/c while the strong peak at low pT < 0.15 GeV/c, that shows up in the experimental data for the mass bins (0.4 < M < 0.7 GeV and 1.2 < M < 2.6 GeV), is fully missed by the PHSD and cannot be explained by the standard in-medium effects. This provides a new puzzle for microscopic descriptions of low pT dilepton data from the STAR Collaboration.