Polarization lost upon 2nd reflection?

A crucial factor is to keep the beam in one plane. Any time you let it wander out of the plane it can rotate the polarization. You will see this if you simply divert the beam upward, then to the right: the polarization will rotate 90 degrees.

Placing as an answer what should be a comment (not enough reputation yet). In which direction is the polarization of incident light?

The "safe" directions are only two, "p" and "s" polarized with respect to the planes of the mirrors; that means, horizontal and vertical.

Edit: now this is becoming an answer.

If your mirror is metallic and the incidence angle is different from zero, the phase shifts for the s- and p-polarized components of the field are different.

Possible solutions:

• rotate the polarization to be s or p before you enter the beamsplitter-mirror setup (if you have a waveplate that does it)
• rotate the source by $45^{\circ}$.