I think it is clear what question is being asked here. There will be a limit on the maximum size of a nucleus stable enough to count as an element, as there are a couple of effects which, at some point, will be insurmountable (and which are also responsible for an isotope of lead being the largest stable element.)
One is that the electrical repulsion of the protons is long-range, while the strong nuclear force binding the nucleons together is short-range. To simplify quite a bit, in a large nucleus, each proton is being repelled by every other one, while it is being bound only by its neighboring nucleons.
The second effect prevents this being worked around by adding more neutrons, as one reaches a point where it is energetically favorable for a neutron to convert to a proton via beta decay.
As mentioned by others, there is likely an 'island of stability' around the largest elements created so far, but this is, at best, only a brief respite from the inexorable effects described above.
The estimates of the half-live of any given element on the island of stability ranges over several orders of magnitude. That being so, it seems unlikely that there is any clear idea which isotope is the largest possible in this universe.
Neutron stars are, of course, very large agglomerations of nucleons, but it seems pointless to call them elements (and there is an upper limit on their size, anyway.)
We give too much importance to the "Periodic Table". It's just a man-made microlang. Nature is unconcerned with it. There is much more beyond it.
P.S. While I'm criticizing the PT, might as well mention that I think we've probably done people a diservice by giving misnomer names like "Hydrogen" and "Oxygen" to these elements, which is completely disconnected from the mathematical beauty and patterns that those names represent.
Wikipedia: Oxygen
> Lavoisier renamed 'vital air' to oxygène in 1777 from the Greek roots ὀξύς (oxys) (acid, literally 'sharp', from the taste of acids) and -γενής (-genēs) (producer, literally begetter), because he mistakenly believed that oxygen was a constituent of all acids.
Hydrogen comes from ‘water’, which contains hydrogen and oxygen.
So, since all acids must have Hydrogen, Oxygen is actually a better name for Hydrogen. This then leaves the name Hydrogen free for Oxygen.
Singtium and Octium, perhaps.
The operating definition has been "a list of all elements that humans have discovered and/or made". By that definition, it is not currently infinite, nor will it ever be.
If instead you define it to mean "all elements that might theoretically exist under all theories of physics that are not currently definitively ruled out", then it may be it infinite. But that's not the normal definition.