I'm a scientist, and have gone to some effort (for reasons you can probably guess) to understand the details behind the tests. If there's some confusion in the above posts about whether Syphilis is curable and what the titers mean, that's because it's damn confusing (many health professionals don't seem to really get the details)! Here's the most accurate information I've been able to glean:
Syphilis is generally *curable* with antibiotics (penicillin), although there are some strains that are resistant (but even these are usually curable with retreatment or stronger treatment).
Entrenched syphilis (stage 2 or 3) is much more difficult to cure than early-stage syphilis. This is at least partly because the bacterium (not a virus) gets into the brain where it is difficult for most antibiotics to reach it (HIV does the same thing). Therefore, if you don't want to have long-term syphilis, it's good to be tested regularly.
The RPR test, and others like it, (the ones that involve the 1:n titer levels) don't actually test for Syphilis or for antibodies to the syphilis bacterium per se. They test for antibodies to a substance that is found in heart muscle. When a human is infected with syphilis or any of several other agents, the bacteria cause damage to the cells and some of the substance leaks out, and the immune system forms antibodies to it. Once the Syphilis is cured, the leakage stops and the immune system *may* stop making the antibodies... but no guarantees. How long this takes depends on your specific immune response, but it is at least months and may be years... or never. If that's the case, even though you are cured of Syphilis (or hope so) you will still have a reactive test.
There are more specific tests for Syphilis where they actually look for the bacteria in the blood, but these are not used as a first-line diagnostic because they require lab procedures that are more difficult, slower, and more expensive.
[edit] Oh, yeah... and Syphilis can be really hard to notice if you don't happen to have a chancre in an obvious place. A fact I can confirm first-hand.