The two TB test are part of the standard recommended 2-step PPD test. Inconclusiveness of the first test is NOT the reason you get a second test. Everyone who gets a properly performed TB test will get two test.
The reason this is done has to do with immunological memory. When your body responds to an infection it produces a lot of cells specifically designed to fight that particular infection. After the infection is controlled, most of these cells simply die off. However, a small population persist in the body and are called memory cells. If you are infected again with the pathogen, the presence of these memory cells means that the body does not have to take the time to generate a whole population of pathogen-specific immune cells from scratch. This means the response will be much more rapid and effective, possibly stopping the infection before you even know you have it.
When you are vaccinated for something, you are trying to artificially produce those memory cells without ever having to get sick in the first place. However, the memory cells don't last forever which is why you need to get booster shots periodically for many vaccines. These boosters help to bring memory cell numbers back up to a level where they can prevent infection.
The booster phenomena is why you receive two TB test. In someone who has been infected with TB, memory cells are generated similar as to with any infection. However, memory cells to TB are not as long lived as some other types and it is possible for them to die off within as little as a year. The TB test works by injecting a substance that looks a lot like TB. If you have memory cells (which likely means you had TB at some point), this injection will cause inflammation and give a positive result. However, if a previously TB infected individual's memory cells have died off, it is possible for them to test negative for TB even though they have had it. However, that one TB test is enough to slightly wake up any old memory cells that have become dormant. While in such an individual no reaction will be seen in the first test, if you test them a second time they WILL have a reaction due to the memory cells that the first test woke up.
So in summary, sometimes your body's immune system can "forget" about a TB infection so when an infected individual is tested the first time nothing will happen. However, that first test can quietly wake up the cells that forgot about TB so that if they are tested a second time, there will be a reaction and the test will be positive.
As for having to get it a third time due to missing the check, I wouldn't worry about it. You can get re-tested a couple of times before it will start to distort the results. Furthermore, getting tested multiple times should almost never negatively affect your health.