I greet my relatives and they respond coldly or not at all. Why should I keep reaching out and maintaining the ties when they clearly do not care?
Being met with silence after you have offered a warm greeting stings, and there is no use pretending otherwise. You greet them with an open heart, the reply is thin or absent, and something in you asks a fair question: why keep pouring water into a cup that seems to have no bottom? That is not bitterness in you. It is a tired heart asking for fairness. The Prophet, peace be upon him, answered that question by turning it around.
He redefined what it even means to keep a tie:
“The one who maintains ties of kinship is not the one who reciprocates; rather, he is the one who, when his ties are cut off, still keeps them joined.”
The Prophet (peace be upon him), Sahih al-Bukhari (5991) · meaning
Notice what he singled out. Warmth that answers warmth is good, but it is common; it is a trade. What he praised is the warmth that keeps flowing when nothing flows back. So your situation is not evidence that you are failing at kinship. It is the very circumstance in which the greater reward is earned.
Nor are you carrying it alone. A man came to the Prophet, peace be upon him, with your complaint almost word for word: he kept ties with relatives who cut him off, he was kind while they were harsh. This is the answer he received:
“So long as you continue as you are, there will remain with you a supporter from Allah against them.”
The Prophet (peace be upon him), Sahih Muslim (2558a) · meaning
Consider what that means. Your one-sided kindness, offered quietly, draws down the aid of Allah, so that a supporter from Him stands beside you. You are not the weaker party here. The coldness stays with them; the support stays with you.
The Qur’an names such people among those it praises:
“And those who join what Allah has commanded to be joined.”
Qur’an, Ar-Ra’d 13:21 · meaning
This is your standing, if you keep it. And there is something the world has noticed as well: steady, undemanding warmth, held patiently over years, will often soften a cold family in a way that confrontation never does. Frost does not lift for a raised voice. It lifts slowly, for the sun that keeps rising whether or not anyone thanks it. So keep rising, not for their reply, but for your Lord, who sees and aids and counts every unanswered greeting you send.
One small step: The next time you greet them and receive only coldness, do not shorten your greeting in return; offer the same warm salam once more, and remember as you do that Allah is with you in that moment.