I would consider a sentence identical to the one we’re examining to be true; you’ll note that the sentence we’re examining contains the word “zebra” seventeen times.
More precisely, there are ways to discuss a sentence that don’t involve discussing its truth or falsehood. If you want a paradox, I think you need to rephrase the OP:
“When X eventually commits to an absolute position regarding truth of this sentence, X will not declare the sentence to be always true.”
where “an absolute position” is defined as either “always true” or “always false.”
Logic majors can gussy that correction up with proper jargon, but I think the basic principle applies:
As long as I’m allowed to discuss such a sentence without committing to its truth or falsehood, then such a sentence can be true as long as I don’t commit to a position regarding its truth in the post in which I discuss it. Interestingly, such a sentence can’t be false: if I commit to a position regarding such a sentence’s truth, then we get a paradox.
One final note. Your sentence does not, of course, contain the word “zebra.” The fact that I incorrectly suggested that it does in no way affects the sentence’s truth; all it does is satisfy this post’s need to discuss the sentence.