What quality would an interactive proof executed many times sequentially have that makes it zero knowledge that one executed in parallel would not? The first protocol can be proved ZK, but the second is not believed to be so? What quality of the parallelization makes it such that an identical protocol executed in parallel, as opposed to sequentially, would remove its ZK properties?

EDIT#1: The source of the IP's was asked for so I shall say, they are from some course notes of a graduate cryptography course at UCLA, from a few years ago, and given to be based off of the book "Foundations of Crypto" by Goldreich.
Hint: look at the security proof of the zero-knowledge property of the first scheme. I recommend writing it fully and formally, if you want the solution to become clear. It relies on a common "rewinding" strategy, and requires in particular to guess in advance the challenge of the verifier, with non-negligible probability. Now, what happens to this strategy when we consider parallel repetitions instead? Can you see where exactly it breaks down? We can give you further hints if you explain exactly what you tried and tell us where you are stuck afterward.