Does this syllogism prove that matter is eternal. If NO, then where
does it fall short?
At least two core, mutually independent issues invalidate the rationale you outline. One has to do with the questionable veracity of P1, and the other is the mistaken extrapolation to the future in P5 notwithstanding that hitherto you had only talked about the past (P1, P3, and P4) or the present (P2).
The other answer addressed P1 from an empirical or somewhat physical approach. The drawback of that approach is that the same argument would improperly negate many other concepts on grounds that no one has ever perceived them. Consider the number one or the addition: We certainly see their representations or symbols ('1' and '+', respectively), and by manipulating both concepts we develop thoughts, calculations, and proofs. However, neither we have ever seen the number|operation itself nor have we ever grasped --let alone in isolation-- the essence of addition as a concept on its own.
P1 pretty much paraphrases one direction of one of Epicurus's most important assumptions. He characterized Creation as an impossibility, arguing that the transitions to and from the states of not-being and being would result in a generalized instability and a constant switching from the being state back to the not-being state. To my knowledge, though, Epicurus never actually proved the validity of his conjecture, nor did he substantiate it much further than along these lines. Thus, the entire rationale is uncertain because it stems from an unverified --if not unverifiable-- premise.
The second issue is the improper extrapolation to the future. P1, P3, and P4 are expressed only in terms of the past (or with a connotation thereof): "come from", "was never at any point", "it's always been something", respectively. Next, the rationale unjustifiably leaps by characterizing the [universe] material as eternal (and, impliedly, endless), without substantiating whatsoever why something that "has always been something" will necessarily continue to exist [in one form or another] forever. At least Epicurus's questionable assumption negates the transition from either state to the other, whereas P1 only negates the transition from not-being to being (leaving the other direction unaddressed).
One mathematical equivalent of the aforementioned, mistaken extrapolation is the incorrect presumption that if an interval has no lower bound, then it has no upper bound either.