About the usage of term 'come again'

Last week I was attending a communications training program. The trainer said that the term 'come again' has sexual meaning in American English. I was surprised as I have seen many Americans using the term in movies and meetings. Is there any such negative sense to the phrase?

Sure, this phrase has sexual connotations, inasmuch as the word come has sexual connotations. But only someone being intentionally perverted would think of sex when hearing the phrase "come again", or another phrase with come in it, in day-to-day situations.

In US English, it certainly doesn’t have a sexual meaning, as other answerers have noted; it’s a common idiom.

However, in UK English, it’s much more likely to be heard/used a double entendre. It’s a much less common phrase in the UK, and since its idiomatic meaning is not terribly transparent, someone unfamiliar with it and trying to parse it literally will almost certainly at least consider the sexual meaning (since most other meanings of come require an implied indirect object, whereas in come again it appears to be completely intransitive).

Certainly the double meaning was a common source of jokes among my student friends in the UK about 10 years ago!

"Come again" is a slang, shorthand for "say again" or "could you say that again", of a longer form and more polite, "could you repeat what you just said, please?"

People who do not know American slang very well say things like: "Could you come again, please", which is wrong, because you are mixing formal politeness with a curt, abrupt slang or "say again".

Foreigners should just ask, "say again" or be formal and say "Could you please repeat that for me, please".

So when you hear someone say "Could you come again, please", it sounds so awkward, that the first thing on one's mind is that they are intending something possibly lurid from the comments, or they would not have added "please" in the phrase with the word "come".

BTW the vulgar word is spelled cum not come.