날 한 번이라도 사랑한 적 있어?

The line, explained

Here is the question nobody wants to ask and every drama eventually does. Two people at the end of something. One of them has been holding it in for episodes, and finally: did you ever love me, even once? The ending -(으)ㄴ 적 있다 is the engine of the line. It does not ask what happened last week; it asks whether a thing has ever happened at all, anywhere in the whole history of the two of you.

날 is 나를, 'me', with the object marker squeezed in. 나 is I or me, 를 marks the object, and together in speech they become one syllable, 날. You met the same contraction in 널 (너를, you) and 누굴 (누구를, who). Putting 날 first puts the speaker at the centre of the question: it is me we are talking about, not the relationship, not the timing, just me.

한 번이라도 is where the ache is. 한 번 is one time, once. 이라도 means 'even' or 'at least', the version of 라도 that follows a consonant. 한 번이라도 therefore means 'even once' or 'even one time'. The speaker is lowering the bar as far as it will go. Not always, not often, not for long. Just once would be enough to make the past mean something, and that is what they are asking for.

사랑한 적 있어? is the grammar point. 사랑하다 is to love. Take the stem 사랑하, attach -ㄴ 적 (because the stem ends in a vowel), and add 있어 for 'is there'. Literally, 'is there an occasion of having loved'. The pattern 적 있다 asks about experience across a whole life: 한국에 간 적 있어? have you ever been to Korea; 울어 본 적 없어, I've never cried. For consonant stems use -은 적: 먹은 적 있어, I've eaten it before.

Compare it with the simple past. 날 사랑했어? asks 'did you love me?' and points at a particular time. 날 사랑한 적 있어? asks whether the fact exists anywhere at all. That is why the drama version is the second one. Say it quietly, with the weight on 한 번이라도: nal han beo-ni-ra-do sa-rang-han jeok i-sseo. The answer the scene is waiting for is 있어 or 없어, and both of them hurt.