I've been doing a lot of amateur research lately (youtube videos) on particle physics and find it all really interesting. I'm also a crazy alien conspiracy theorist who believes in the whole "Bob lazar story" which I won't elaborate on in this thread.
Anyways, from my understanding, new elements can be created by shooting a proton into a nucleus and having it get close enough to the nucleus that the strong force overpowers the repulsive coulomb forces between the protons (this is what happens in stars with fusion). This is difficult because the proton needs enough energy to be able to pierce the electromagnetic repulsion of the nucleus. On the other hand, if you want to create an isotope of an element, this is easier because neutrons are electrically neutral and are unaffected by the electromagnetic force. So all one needs to do to create an isotope is have the neutron come within a close enough range of the nucleus for it to react and be absorbed.
So lets say we have some unstable nucleus that will typically decay after 50us. If I were to shoot a neutron into this nucleus and it reacts successfully, from my understanding it would become a new isotope with a new rate of radioactive decay. This is a bad example because I am making up numbers, but lets say the new isotope becomes even more unstable and decays after 40us. If the neutron was initially shot into nucleus 1 25us after the creation of nucleus 1, would nucleus 2 "be at 25/40% the way through completing its radioactive decay? Or would the "atomic decay clock" reset so to speak?
I know that this is a gross simplification of nuclear decay, and that in reality it is more probabilistic than determinate. The reason I'm asking this is because I want to understand why we couldn't just keep shooting neutrons into a super heavy element until we find a stable isotope. Even if it were to decay near instantly, it shouldn't be impossible for us to create a high enough flux of neutrons for it to continuously plug neutrons into an element if this were the case.