I mentioned the Hubble Deep Field to counter your "greater distances will yield less visible light" argument. Pointing the Hubble at a pitch black portion of space and witnessing thousands of galaxies seems to be a pretty strong argument towards the infinite shelf life of light. According to how you presented your argument, we should be unable to see anything in a pitch black portion of space, but we did.

If anything, humanity has shown that limits fail to contain us. Several hundred years ago we were unable to clearly see our neighboring planets and today we can look as far as 13 billion years, do you really think humanity is going to stop reaching and striving for more?