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Is the polarization of a light beam permanent? I mean, does the polarization change as it travels through vacuum?
If so, what causes it to change?

Circular polarization is related to the spin angular momentum of photons. A spontaneous depolarization of a circularly-polarized beam would probably violate conservation of angular momentum. (But you can transfer the angular momentum to another system. My favorite classic physics paper, Beth (1936), describes using circularly polarized light to drive macroscopic mechanical oscillations in a torsion pendulum.)

Linearly polarized light is a coherent superposition of the two circular polarization states, with the direction of the linear polarization determined by the relative phase of the left- and right-circular components. Interactions between light and the interstellar/intergalactic medium could cause the two circular polarization states to see different effective indices of refraction, which would cause the plane of the linear polarization to rotate. The biggest such effect is probably Faraday rotation, which occurs when light travels through a medium with a magnetic field parallel to the direction of travel. That's a change in the direction of the polarization, rather than a change from polarized to unpolarized light, which is the kind of thing you asked about but not exactly what's in your question title.

This 2012 paper by Trippe and collaborators discusses the absence of polarization in radio emissions from a quasar as evidence for a complex interstellar medium around the active galactic nucleus; it might suggest to you several other search terms, and it's got a nice set of references.

I have the impression that your question is more about interactions far from any matter, though. I think it's possible that, even in the most tenuous parts of the intergalactic medium, and far from any Faraday-rotation-causing magnetic fields, there might still be some optical activity to the vacuum. This is because light actually participates in the electroweak interaction, rather than just the electromagnetic interaction, and mirror symmetry is not a good symmetry of the weak interaction. However, optical rotation due to the parity-violating vacuum would be very challenging to separate from Faraday rotation due to magnetic fields along the path taken by light as it approaches you. Furthermore I can come up with hand-wavy arguments about why the optical activity of the vacuum both should and shouldn't be exactly zero. So it's probably safe to file that idea in the "hmmm" pile for now, and address it in a separate question if necessary.

The polarization doesn’t change as light travels through a vacuum. Neither does the frequency or the wavelength (unless you take the expansion of the universe into account). We can measure the polarization of the cosmic microwave background, which has been unchanged over the 14 billion years that the microwaves have taken to reach us!