Is it theoretically possible for the output of SHAKE to be an infinite concatenation of the same 512-bit block?
Minor correction: SHAKE generates either 1088 or 1344 bits per squeeze; not 512.  So, the example you give will give a repeating pattern, but it'd be either 3264 or 4032 bits long, not 512.

Other than that, yes, that is possible, as far as we know.  In fact, a far more likely repeat is:

$$\operatorname{Keccak-}f(A||X) = A||X$$

This would give a repeating pattern of 1088 or 1344 bits long.

In addition, not only is this possible, there's a good likelihood that there actually is such a $A || X$ pattern.  Such a $A || X$ is known as a fixed point of the permutation; a random permutation has at least one fixed point with probability approximately $1 - 1/e \approx 0.6321$; assuming that $\operatorname{Keccak-}f$ does, in fact, act like a random permutation, then it's more likely than not that there is such a fixed point.