I can think of a couple of fics where Sesshoumaru breaks up with Kagome because of rumors/lies.
A Heart's Recompense by Time on my hands
Lies and betrayal. Both of them were victims of the single-minded obsession and unreasoning hatred of another. Will they ever find their way again? It's possible. If the recompense is great enough.
Rated MA
Something To Talk About by KogasAngel
*Final Chapter* Because of Ayame's lies, Kagome must prove to Sesshomaru that he fathered her pup. When the truth comes out, Kagome is given the chance of a lifetime and decides to take her fate into her own hands.
Rated MA (NC-17)