I believe this is Please Marry Me Again!.
From Baka-Updates:
As a so-called "half-noblewoman", Shurya Littenheim was shunned by all in high society except her husband, Grand Duke Kardi Esperand. So when the powers Kardi inherited from his family start to slowly kill him, Shurya gladly makes a deal to sacrifice her own life instead. Upon her death, she's reborn as her younger, single self, and this time... she's doing it all over again! Shurya's on a mission to make Kardi her hubby once more, but is there any hope of avoiding yet another tragic ending?
The main character, Siera Littenheim, is the illegitimate daughter of a duke and most of her family despises her, so she arranges a political marriage with a prince, Kardi Esperand, to get away from them.
Kardi thinks of himself as a monster as he has a power passed down through his bloodline which makes him a formidable weapon for his father on the battlefield, but drains his lifespan, such that he isn't expected to live past 30. Siera falls in love with him, and makes a secret deal with his father to share the burden of Kardi's power, so that her lifespan would be shortened instead of his.
Kardi subsequently learns of this arrangement when she dies ten years after their wedding and is heartbroken, wishing he could see her just one more time. She then wakes up back in her father's mansion, shortly before her wedding with Kardi.
