When you first started the conversion process, did you know that it's permanent?
That is a good point that some conversion candidates may not discover for a little while. I can't imagine that any movement would convert someone without making sure this is understood. But since we're talking about conversion, let's talk about it.
Once you convert, you are a Jew. Forever. And ever and ever. Even if you suddenly decided Judaism was a phase, and you wanted to become a Hindu, Wiccan, or Buddhist. Even if you returned to a prior religion. If you convert orthodox, this means even if you decided to join a liberal movement. And even if you decided to no longer affiliate Jewishly but don't join a new religious group. You're Jewish. Period. End of story.
If you do those things, you are halachically still a Jew. You're just a bad Jew :P
Of course, you are probably wondering about those stories of conversions being overturned or "taken away." If you were not sincere at the time of your conversion in agreeing to take on the mitzvot, and I really mean at that time only, the conversion can be nullified. That's not overturning it; it's as though the conversion never existed. Halachically, if you were sincere up until the day after your conversion, you're still Jewish. That's hard to measure.
Some groups have made a "testing" time (so to speak), and they will refuse conversion papers or seek to nullify a conversion if the convert abandons Judaism (or if orthodox, the observance of mitzvot, even partially) within 1 year of the conversion. The idea is that if you weren't sincere at the time, you should show your true colors by then. If they withhold your conversion papers, you're unable to prove the conversion occurred. Your papers are essential to the rest of your Jewish life. In practice, if you can actually manage to fake it for the 2-5 years currently required for orthodox conversions, you can certainly fake it for one more year.
You're probably still confused. Why have you heard of so many conversions being overturned? It's not common at all, but there is definitely a fear of "de-conversion" within the convert community. I'm not going to lie, it even frightens me. But in the grand scheme of things, you're probably going to be just fine. Keep reading.
There are primarily two situations in "de-conversions."
A) The more likely is that a member of the beit din later becomes disqualified from sitting on a rabbinical court. Several reasons could create this issue, but you probably won't be told why because that would be lashon hara. Generally, it must be regular violation of basic halacha like Shabbat. They will then have to determine how long this has been an issue. Any court he sat on during the time he was possibly disqualified, there is a risk that the beit din wasn't properly convened. In short, it's a procedural issue. There is nothing wrong with you. The situation is easily remedied with a geirus l'chumrah, which is just a second conversion ceremony without the blessings said in the mikvah. Chumrah means stringency. This is "just to be safe." And it's essentially retroactive. This can be emotional for some, but it's not a big deal in the grand scheme of things.
The second situation would definitely make you feel upset and betrayed.
B) This is an issue of the usual suspects who rule their communities with an iron fist of conformity. A woman starts wearing pants or covers her hair in a way not accepted by "the community," and suddenly the rabbi is yelling that she must not have intended to take on the mitzvot at the time of her conversion, even if it was 15 years ago. This is definitely more of an issue for women than men. In general, if he is the rabbi who converted you, he can singlehandedly claim that your conversion was invalid. That doesn't mean another rabbi will accept his claim of invalidity. If he wasn't your converting rabbi, he needs to convene a new beit din to rule on the issue. Again, that doesn't mean that another rabbi will accept their ruling as valid. Of course, he can forgo the beit din and ostracize you from the community, telling everyone your conversion is not accepted as valid in the community. In the very unlikely event this happens, you can simply change communities. The problem occurs when you don't have an option you want nearby but lack the funds/ability to move. In that case, I'm afraid that I'm no use, but you should contact any rabbi you feel comfortable with. I'm sure he would be pleased to talk with you and discuss your options. One possible option if you move is to also have a geirus l'chumrah if this is your converting rabbi so that anyone who needs to verify your conversion won't call him to verify the validity of your conversion. Of course, he will tell them it's not valid. If you have a geirus l'chumrah, the most recent beit din is who will be contacted for verification of your Jewish status. That said, most rabbis know which rabbis do this sort of thing. That's why I call them "the usual suspects."
So in short, once you're in, you're in. Understand that and live up to the challenge. And even though it isn't fair, remember that your actions post-conversion reflect on all other converts, as well as the rabbis who converted you. You're not an island in Judaism, and the conversion community needs you to stand with us.