Well, obviously you can't translate many things literally, as you would constantly end up with sentences such as "it gave it to it" in English, where in the source language with genders you have a perfectly clear "she gave it to him".
However, there are usually easy ways around this, the most obvious one being: kick out the pronouns and replace them with nouns. "The cat gave it to the kitten." If anything, you gain meaning by doing that (though you might waste quite a few syllables if you're translating a poem).
To me, this question sounds a lot like "How could one possibly translate from English to a language that doesn't have articles?" To which any professional translator should answer: "Without breaking a sweat".
[Disclaimer: I am a native speaker of two languages, one with genders but without articles, and one with genders and articles.]
Here's an example I should have thought of right away. It is still not quite what you are looking for, but I'm getting closer step by step.
Imagine any TV show where several candidates compete for whatever the prize is. The host is about to announce who is going to proceed to the next round. He says, "I have good news for one of you", or "The last one to reach the final is...", or something to that extent. Now, in many languages with genders he could give a subtle hint by using either the female or the male form of "one" (un/une, einer/eine, один/одна, um/uma, etc.). In English, the equivalent would be something along the lines of "I have good news for a male candidate", or "The last one to reach the final is a female, and her name is...". Which, of course, wouldn't be anywhere as succinct, and not subtle at all. The closest you could get to that kind of hint in English would be "I have good news for you guys", or "The last one of you gals to reach the final is...", but that still doesn't quite cut it (even if we ignore for a moment that guys does not necessarily refer to males).
In fact, in order to avoid giving any hints accidentally, in those languages it is quite common for the host to say "I have good news for one or one of you", or "The last one or one to reach the final is...", where the first one is the male form, and the second one is the female form. When translating that into English, you'd just drop one of the ones, so that one or one become one — which, of course, is more succinct without losing meaning, but the original expression is not really translatable "as is".
Here's yet another example.
In German, a language with grammatical genders, there is quite a lot of confusion going on whenever you want to say that Angela Merkel is the first chancellor to do something. Normally, Angela Merkel is referred to as die Bundeskanzlerin, a female form of the noun der Bundeskanzler, or "female chancellor" for short. So, naturally, the first thing you try is "Angela Merkel ist die erste Bundeskanzlerin, die X macht" ("Angela Merkel is the first female chancellor to do X"). However, that sounds kind of pointless, because Merkel is the first female chancellor ever, so no matter what she does, she can't help being the first female chancellor to do it.
In order to avoid that pointlessness, journalists sometimes use the male form of chancellor: "Angela Merkel is der erste Bundeskanzler...". Grammatically, this is probably the most sensible thing to do. However, to many Germans this sounds strange, and even funny, much like saying "Angela Merkel is the first man to do X".
In order to avoid that confusion, some political commentators bring the adjective weiblich ("female") into the equation: "Angela Merkel ist der erste weibliche Kanzler, der X macht". However, this brings us right back to where we started ("Merkel is the first female chancellor to do X"), in addition to introducing yet another bit of humor, because the sentence now reads much like "Merkel is the first female man to do X".
As if that weren't enough already, some political commentators completely overdo it by using both the adjective "female" and the female noun, as in "Angela Merkel ist die erste weibliche Bundeskanzlerin, die..." ("Merkel is the first female female chancellor to..."). This, of course, is the most stupid thing they could possibly do, but it's also the funniest, since it sounds much like "Angela Merkel is the first female woman to do X".
I am fairly confident I could come up with lots of similar examples in other languages with grammatical genders (say, French or Russian). By not having genders, English completely avoids that type of confusion, but it also misses out on all the humor associated with it.