You're assuming that nuclei with exactly a magic number of neutrons are more stable than all their non-magic neighbors in the chart of nuclides, but there's no reason to think that.
If a nucleus has a magic number of neutrons, that means one shell is completely full, and the next shell is empty. Therefore the next neutron you add (going to magic+1) will have significantly greater single-particle energy, so that nucleus should be less stable than the magic one. This is born out by both of your examples for the well-known magic number 126:
- Po-211 (N = 126+1): 0.5 seconds
- Ra-215 (N = 126+1): 1.5 milliseconds
However, if you remove one neutron, then nothing changes about the other (magic−1) neutrons; they are still in the same shells as in the magic case. No extra stability is caused by having a completely full shell as opposed to an almost full one. (In this respect, the word "magic" is misleading.)
Here's another way to think of it: In alpha decay (which is the main decay branch for all of your examples), two neutrons are removed from the nucleus. It will always be the two most energetic neutrons that are removed (those in the highest shells). In a magic nucleus, the lower shell is completely full, so two neutrons are removed from that lower shell. In a magic+1 nucleus, there is a lone neutron in the upper shell, so when two neutrons are removed, one comes from the upper shell and one from the lower shell. Since one comes from the upper shell, more energy is released in the alpha decay and in general the half-life will be shorter.
However, in a magic−1 nucleus, there are no neutrons in the upper shell, so both neutrons come from the lower shell. This is the same situation as the magic case, so there's no reason to expect the decay energies or half-lives to be drastically different. (Of course they won't be exactly the same, but the differences come from other, more subtle effects.)
BTW, 152 is not a "canonical" or "universal" magic number. It shows up on the plot you have there of some specific elements, but if you look at other elements, the gap between the shells occurs at a different place. 126 is a universal magic number, but at 152 the situation is more complicated because changing the neutron/proton ratio also shifts the shells relative to each other. This is why the thing I said about magic+1 always being less stable than magic doesn't hold for one of those. Nuclear structure is really complicated.
This is really a comment, since I don't think there is an answer to your question, but it got a bit long to put in as a comment.
If you Google for "Why is technetium unstable" you'll find the question has been asked many times in different forums, but I've never seen a satisfactory answer. The problem is that nuclear structure is much more complex than electronic structure and there are few simple rules.
Actually the question isn't really "why is technetium unstable", but rather "why is technetium less stable than molybdenum and ruthenium", those being the major decay products. Presumably given enough computer time you could calculate the energies of these three nuclei, though whether that would really answer the "why" question is debatable.
Response to comment:
The two common (relatively) simple models of the nucleus are the liquid drop and the shell models. There is a reasonably basic description of the shell model here, and of the liquid drop model here (there's no special significance to this site other than after much Googling it seemed to give the best descriptions).
However if you look at the sction of this web site on beta decay, at the end of paragraph 14.19.2 you'll find the statement:
Because the theoretical stable line slopes towards the right in figure 14.49, only one of the two odd-even isotopes next to technetium-98 should be unstable, and the same for the ones next to promethium-146. However, the energy liberated in the decay of these odd-even nuclei is only a few hundred keV in each case, far below the level for which the von Weizsäcker formula is anywhere meaningful. For technetium and promethium, neither neighboring isotope is stable. This is a qualitative failure of the von Weizsäcker model. But it is rare; it happens only for these two out of the lowest 82 elements.
So these models fail to explain why no isotopes of Tc are stable, even though they generally work pretty well. This just shows how hard the problem is.
Best Answer
As noted in the comments, all of the various Cs isotopes I'll mention decay by emitting a beta, converting the Cs isotope to a Ba isotope. Now, while details of nuclear decays are not necessarily touched on unless you are in a nuclear physics course, they are at least somewhat analogous to electron or photon decays. What I mean by that is that you are, at a hand-waving level, looking at an initial state (the Cs), final states (Ba in various possible energy levels), and any applicable quantum numbers you would like to try and conserve (like nuclear spin).
So, let's take a tour of the isotopes, relying mainly on data from nuclear datasheets. Start with Cs-134 (you probably did not know there was a journal called Nuclear Data Sheets). Going down to page 69, one finds that the Cs-134 nucleus has a spin of 4. It can decay to any one of 6 possible Ba-134 nuclear energy levels (the ground state and 5 excited states). The majority of the decays go through an excited state, which also has a nuclear spin of 4. The half-life is 2 years.
Cs-135 is listed with a nuclear spin of 7/2. There is only one available Ba-135 level to decay to, and it has a nuclear spin of 3/2. The half-life of this decay is 2.3 million years. Only one state to go to, and a spin mismatch to slow it down.
Cs-137 has a nuclear spin of 7/2. It can decay into 3 different Ba-137 levels, the ground state, and two excited states. The majority go through an excited state with spin 11/2. The other two states have spin 1/2 or 3/2 (the ground state). So, a few more states to decay to, but some pretty large spin mismatches on several of them. The half-life is 30 years.
Cs-139 has a nuclear spin of 7/2. It can decay into one of 60 (!) different Ba levels, with most decays being to the ground state which has a spin of 7/2. The half-life is 9 minutes.
Taken all together, what do we see?
More available levels to decay to increases the chance of decaying. Closer spin values between the parent and daughter nuclei increase the chance of decaying. To go much deeper requires diving deeper into nuclear physics.