They die on their own
This race isn't immortal, just really hard to die. Because of this they have long come to the conclusion that they will die eventually and instead of trying avoiding it, they march to their deaths once they decide it is worth the risk. This race is full of glory seekers who would rather die doing what they love or fighting for what they believe in than by the many accidental deaths that could happen like drowning or starvation (everything is likely if you're going to repeat it forever), which in turn make them die earlier.
Strong body, weak heart
Maybe mental health keep deteriorating with time, and I am not talking abou memory or sanity. Happiness is such a fragile and fleeting thing, one day you are the luckiest man in the world, the next day the love of your life elope with her secret lover and take your child with her, your best friend turn on you for reasons "you know very well" and on top of everything you hear a not very comforting comment about the whole affair from your neighbors. When life just keep going forever, is easy to get tired of it. Even if they don't straight up kill themselves over it, they may just stop bothering with life after a certain age, or even snap and go full psycho. And when it happens, the government can dispose of then in a humane way (literally putting then out of their misery).
I think they have a similar justification for why vampires don't have friends in World of Darkness ttrpg, petty grudges keep adding up and become spite.
Enforced birth control
Simply put, it is illegal to have a child without the government permission. Couples must apply to get the permission, until then and for those who don't want kids anyway, there are options ranging from normal contraceptives to induced infertility.
In dnd, elves have a magical version of this. Instead of a government, there's a set amount of elven soul and the elf deity recycle the soul of the dead to use in the future new borns. If there's been happening too much births, its probably because something bad is going to happen (if they didn't need extra numbers, the deity wouldn't expend the emergency stock). That's also why they don't go extinct for lower fertility rate after tragedies, if there's extra souls lying around, the birth rate increase to compensate.