The beam-recoil double polarization P(x')(h) and P(z')(h) and the recoil polarization P(y') were measured for the first time for the p(e,e'p)eta reaction at a four-momentum transfer of Q(2) = 0.1 GeV(2)/c(2) and a center of mass production angle of theta = 120 degrees at the Mainz Microtron MAMI-C. With a center of mass energy range of 1500 MeV<W<1550 MeV the region of the S11(1535) and D13(1520) resonance was covered. The results are discussed in the framework of a phenomenological isobar model (Eta-MAID). While P(x')(h) and P(z')(h) are in good agreement with the model, P(y') shows a significant deviation, consistent with existing photoproduction data on the polarized-target asymmetry.