What could explain the presence of Technetium in the spectral lines of stars? So, I understand that TC doesn't exist in nature [though, I don't know why every reference I see regarding TC says that and then goes on to state that it is found in some stars...] but, if that's the case, then why is it found in some stars? Furthermore, why is this element skipped during the regular process of nucleosynthesis? And, why do some stars magically fuse technetium while others don't? Lastly, how many technetium stars have been discovered? Thanks much.  
***Just a note, I was just looking at this all again and started thinking about how Technetium is way heavier than iron, so it's not formed in regular nucleosynthesis, right? Which means the TC is left over from supernovae explosions, right? So, if that's the case, why is it not produced naturally? What is natures aversion to this element? 
 A: This is really the same as my answer to your later question (I saw the later question first).
Technetium is thought to occur mainly by slow neutron capture. Repeated neutron capture in a complex chain of reactions eventually produces Technetium. There are details of the reactions in this PDF.
There is a paper here suggesting that it may also form from heavy nucleus fission, just like Promethium. However the paper is behind a paywall.
A: As John Rennie correctly says. Tc is formed by neutron capture in the s-process along with many other heavy chemical elements (Ba, Sr, Eu, Pb etc.).
The conditions for the s-process require a neutron source. This is provided by alpha capture onto carbon 13, or sometimes neon 22 in more massive stars.
A plentiful supply of carbon 13 only exists (at the right sort of temperatures and densities, and there are other requirements too) inside asymptotic giant branch stars with helium and hydrogen burning shells. The AGB phase occurs near the end of the life (they end up producing white dwarfs) of most stars of less than about 8 solar masses.
The neutrons are captured in a chain of reactions by pre-existing iron-peak nuclei in the star to make the s-process elements. However, to be visible in the photosphere there also needs to be the right conditions to dredge up material to the surface.
The models of these events are complicated. The details depend exactly on the evolutionary stage, the overall metallicity of the star and more. This is thought to be why Tc is only seen in some AGB stars. More details as and when I find them...
Ah, but the other crucial point is the half life is short, so even when manufactured in AGB stars, it is not "passed on" to the next generation of stars - so it is not generally observed in most stellar spectra.
A: Technetium is not found on Earth in chemically significant quantities because its most stable isotopes (Tc-97 and Tc-98) have half-lives of about four million years. Any technetium that was incorporated into the Earth when it formed, four billion years ago, is now diluted by a factor of roughly $2^{-1000}\approx 10^{-300}.$  The earth only contains $10^{40}$ or $10^{50}$ atoms (heck, the universe only contains $10^{80}$ atoms). All the primordial technetium is gone.
Any technetium on Earth must have been produced by nucleosynthesis sometime in the last few million years.  The most probable sources are neutron capture on molybdenum and uranium fission.  Some of this does occur naturally. Cascades from cosmic ray collisions produce free neutrons in the atmosphere and in the ground: we get carbon-14 (which is much shorter-lived than technetium, only about 5000 years) from the reaction $\rm ^{14}N + n \to p + {}^{14}C$. Natural uranium also undergoes "spontaneous fission," but the large number of stable molybdenum and ruthenium isotopes means that the only long-lived Tc isotope to appear in uranium fission products would be Tc-99.
Stars are different, though, because the temperature in stars is hot enough to boil nuclei. There are plenty of free neutrons inside a star, not from cosmic ray collisions, but from the energetic nuclear reactions which make the star shine. These neutrons will capture on any nucleus floating around in the star.  If the captures are slow relative to typical beta-decay lifetimes then most of the nuclei produced will be stable; this slow capture is called the "s-process" and can produce nuclei as heavy as lead and bismuth.  That capture-decay-capture route includes technetium. In fact, technetium concentration (especially ratios of Tc/Mo and Tc/Ru) would be an interesting way to explore the s-process in a star, since every technetium nucleus has interacted with a free neutron in the past few million years.
So the short answer is that stars may contain trace amounts of technetium and other short-lived isotopes because stars are actively transmuting elements in large quantities.
