I'm not informed on PET specifically, but my understanding was that most plastics can only be recycled once, and that the recycling process generally can't produce the same grade of plastic as the input material.
Have a look at https://egreen.co.uk/brochure/index.html#p=32 for an example of clear drinks cups made from 100% post consumer waste.
Polymers can degrade, but if it's well managed then generally not a problem and I think it can be recycled more times than paper. Each time that is processes the fibres are broken so it the strength is affected. The lowest grade is toilet tissue which has almost no strength compared to something like virgin Kraft with very long fibres.
One thing to consider is recycling is advancing at a phenomenal rate, what was the case five years ago may no longer be an issue.