I very much like shelanachium's answer, but I will add a bit on a point he briefly touched on if it helps any.
There is a general trend that atoms with even atomic numbers have more stable isotopes than those with odd atomic numbers. If you flip through a book that lists all of the stable isotopes for each atom (a good one to do this with is Elmsley's "The Elements"), you will notice that the atoms 1~88 with odd atomic numbers have 1 or at most maybe 2 stable isotopes listed for them. For example, Manganese has an atomic number of 25 and only 1 out of the 4 isotopes listed is stable, and Iodine has an atomic number of 53 and only 1 out of the 5 isotopes listed is stable. In contrast the atoms with even atomic numbers tend to have two or more than two stable isotopes (and sometimes many more). For instance, Magnesium with atom number 12 has 3 stable isotopes out of the 4 isotopes listed, and Selenium with an atomic number of 34 has 6 stable isotopes out of the 7 isotopes listed.
The reason for this likely has to do with the nuclear packing of the protons (which are equal in number to the atomic number). If you have an odd number of protons you can't arrange them in a symmetrical pattern very easily. To get a feel for why this is try making a symmetrical object like a large square by stacking small square blocks closely together. You will find that you can only make "smooth" squares by using an even number of blocks; if you use an odd number, there will always be a "zit" hanging out somewhere in your arrangement.
For the nucleus, having an odd "man" out (or proton in this case) means that the process of introducing neutrons to try and "fix it" is harder than it would be if you just had an even number of protons to start out with. The evidence for this is that these odd numbered atoms tend to be much more sensitive to the number of neutrons present than the even numbered atoms are. For example, for Cobalt if you have exactly 32 neutrons present, then the isotope is stable. On the other hand, Cobalt is unstable if you have 33, 31, 30, or 29 neutrons present. For even numbered atoms the number of neutrons present is usually much less of an issue as can be seen with Neodymium which is stable if it has 82,83.85,86,88, or 90 neutrons while only configurations with 84 and 87 neutrons are unstable.
So what does this all mean for technetium? It means that it is just statistically unlucky for the most part. Unlike Cobalt which can cover up the problem with that *perfect* number of neutrons so that it has *at least one* stable isotope, none of the numbers of neutrons available to technetium can be arranged in such a way to make technetium isotopes stable. If we "outlawed" 32 neutrons in the nucleus, then Cobalt too would be in the same category of "stability" as technetium because all it's other neutron possibilities are unstable. Some odd numbered atoms such as Bromine are "above the average" as they ended up with 2 isotopes that are stable, many like cobalt had only one stable isotope, and some like technetium ended up "below the average" and had none. I suppose that's just the way things go in this world.
Hope this helped.