For a natural-born citizen, the only realistic way to lose your citizenship is through voluntary renunciation. To do that, the person must be over 18 years old, and must appear in person at a US consulate. It cannot be done on US soil, it cannot be done under duress, it cannot be done by anybody under 18, and it cannot be done by anybody but the person themself.
This is actually a problem for some children born on US soil to Indian parents who plan to return to India. India does not allow dual citizenship, and requires that the child renounce their US citizenship in order to retain Indian citizenship. But that is impossible to do under US law.
I believe there also are theoretical mechanisms that could be used in cases of treason or voluntarily working in a foreign government or enlistment in a foreign military, but in practice I don't think this ever happens. The Supreme Court made a series of decisions that basically threw out most, if not all, of these laws.
In real life, there are quite a few US citizen foreign dignitaries. Queen Noor of Jordan comes to mind. Also, Mohamed Abdullahi Mohamed became President of Somalia while still a US citizen (he later did renounce his US citizenship).
That doesn't mean that the US government hasn't tried extralegal means to strip somebody of US citizenship. During WW II, many Japanese-Americans had been pressured to renounce their US citizenship. Those renunciations were all later overturned. More recently, the Taliban member Yaser Esam Hamdi was born in Louisiana, and therefore a natural-born US citizen. The US government forced him to renounce his US citizenship. If he wanted to pursue that, that renunciation would be almost certainly be considered invalid, so he probably still is a US citizen. Of course, odds are that this case won't ever end up in any court. It might come up, for instance if he has children who claim derivative US citizenship.
For naturalized citizens, citizenship can also be revoked if the citizenship was obtained fraudulently. That is usually the process used for revoking the citizenship of former Nazis who had failed to disclose their background when they immigrated.