There are numerous traditions to the fact that Sileh Rahmi is obligatory. In one of such traditions Imam Baqir (a.s.) relates from the Holy Prophet (s.a.w.s.) that he said:
"I will (command) all the people of my Ummat, whether present or not, and those generations which are to come till the Qiyamat, who are still in the loins of their father and wombs of their mothers, that they should be kind to their relatives (and visit them) even if they live at a distance of a year's journey. Because kindness to relatives is one of the commands which is made an integral part of the faith (Imaan)."
One Who is Kind to the Relatives Will be Able to Cross the Bridge of Siraat Smoothly
Imam Muhammad al-Baqir (a.s.) relates from Hazrat Abu Zar Ghaffari (r.a.) who quotes the Holy Prophet (s.a.w.s.) to have remarked:
'Siraat (the bridge passing over Hell that everyone has to cross) will have on each side (of it) 'Sileh Rahmi' and 'Amanat' (keeping a trust) one who performs the act of Sileh Rahmi and maintains trusts (Amanat) shall be able to cross the 'Siraat' easily and will reach Paradise.
None of the good deeds will benefit those who have broken ties with relatives or committed breach of trust. They will slip from the bridge of 'Siraat' and drop into Hell-fire.
(Al Kafi)
The Worldly Benefits of Kindness to Relatives
Numerous reports (Rawayaat) testify that Sileh Rahmi (kindness to one's relatives) also has worldly benefits. Like, increase in the life-span, postponement of death, increase in the number of descendants etc., Hazrat Imam Ja'far as-Sadiq (a.s.) related three traditions from the Holy Prophet (s.a.w.s.) in the court of Mansur Dawaniqi (l.a.).
1) "A man who has only three years of life remaining, performs an act of kindness to his relatives and Allah increases his life by thirty years. In the same way a man has thirty years of life but due to his breaking off the ties of relationship, his (remaining) life is decreased to three years. Then the Holy Prophet (s.a.w.s.) said: Whatever Allah wills He erases and whatever He wills He writes.
It means that if Allah wills He can alter (certain destinies) due to one's actions and deeds."
(Behaarul Anwaar)
2) "Fulfilling the rights of kith and kin increases the life-span even if the relative is a sinner."
(Behaarul Anwaar)
3) Sileh Rahmi (kindness to relatives) is a cause for the easy accounting of one's deeds on the day of Qiyamat and it (Sileh Rahmi) protects one from sudden death."
Hazrat Imam Ja'far as-Sadiq (a.s.) has told Maysar:
(O' Maysar) the time of your death has arrived many times but Allah has postponed (your death) due to your kindness to the relatives and good behaviour towards them.
source : GREATER SINS by Ayatullah-ul-Uzma Sayed Abdul Husain Dastghaib Shirazi (r.a.)