Did Kenshin Really Say “Whatever You Lose, You'll Find It Again, But What You Throw Away You'll Never Get Back”?
No. The line is from Rurouni Kenshin, but it is not Kenshin's. Readers of the manga's Jinchū arc credit it to Oibore, the ruined old man in the fallen village who turns out to be Tomoe and Enishi's father. Kenshin is the character it got filed under.
Spoilers throughout. This page assumes you have finished the series.
No, not Kenshin. The sentence is from Rurouni Kenshin, which is why it survives every check that catches an outright invention, but the person who says it is not Himura Kenshin. It belongs to a minor character in the manga's final arc, and it migrated to the hero's name because the hero's name is what people search for.
The verdict
Misattributed. Wikiquote's Rurouni Kenshin page has nothing resembling it under Kenshin or anyone else. Every social post crediting it to Kenshin gives no chapter, no episode and no arc. The one place the line appears with a scene attached is in readers' transcriptions of the manga, where it is credited to Oibore, the old man of the fallen village in the Jinchū arc, speaking to Yahiko and Misao when they come looking for Kenshin. The wording those readers record is also longer and looser than the meme: something close to "if you live long enough, you lose a lot, just as long as you don't throw them away; whatever you lose you'll find again, but what you throw away you never get back." The quotable two-sentence version is a polish of that.
Who Oibore is
The Jinchū arc, the manga's last and the one the 1996 anime never adapted, sends Kenshin into a settlement of the destitute after he believes Kaoru has been killed. The man who shares his corner of it is a nameless drunk the others call Oibore, roughly "old wreck." The reveal, held until late in the arc, is that he is the father of Tomoe and Enishi: Kenshin's father-in-law, in other words, sitting beside the man who killed his daughter without either of them knowing who the other is. Given that, the line about what you lose and what you throw away is his life in a sentence, and giving it to Kenshin flattens it into a proverb. Coming from a father who lost both children to the same swordsman, it is something else.
Why it moved to Kenshin
Three reasons, all ordinary. Kenshin is the character people know, so quote pages attribute stray lines from the series to him the way they attribute stray Naruto lines to Naruto. The arc it comes from was never animated, so the great majority of the anime audience never met Oibore and has no competing memory of the scene. And the sentence sounds like Kenshin's ethics, the rurouni who has spent ten years refusing to throw anything away, including his guilt, so the attribution feels right to people who have not read the volume. Misattributions do not need a conspiracy. They need a famous face and a plausible fit.
What Kenshin actually says
His own lines are on Wikiquote and are blunter about what he is: "a sword is a weapon, the art of swordsmanship is learning how to kill," and the refusal that follows from it, "no matter what the reason, this one refuses to take another life." Those are the sentences that make him; the Oibore line is a sentence about him, which is a different thing. Rurouni Kenshin does not yet have a quote page on this site, so there is no hub to send you to; when it opens, the lines on it will be checked against the same page.
How we checked
The verification process asks for a primary or editorial source. Wikiquote has the series but not the line; no editorial ranking we could find prints it; the only sourced attribution anywhere is the readers' one to Oibore, which we have not been able to confirm against the Viz volume ourselves and therefore report as what it is, a consistent reader attribution rather than a citation. The verdict does not depend on that detail: whoever says it, it is not Kenshin, and it is not in any scene the anime audience saw. It sits in the fact-check database as misattributed, and if the volume proves the readers right, the entry gains a page number.