We report a first study of the depolarization behavior of spin polarized H3 e in a mixture of H3 e- H4 e at a temperature below the H4 e λ point in a deuterated tetraphenyl butadiene-doped deuterated polystyrene (dTPB-dPS) coated acrylic cell. In our experiment the measured H3 e relaxation time is due to the convolution of the H3 e longitudinal relaxation time, T1, and the diffusion time constant of H3 e in superfluid H4 e since depolarization takes place on the walls. We have obtained a H3 e relaxation time of ∼3000s at a temperature around 1.9 K. We have shown that it is possible to achieve values of wall depolarization probability on the order of (1-2) × 10-7 for polarized H3 e in the superfluid H4 e from a dTPB-dPS coated acrylic surface. © 2008 The American Physical Society.