Recently I have come to know that if a person commit and persist in major sin and die in that way without Taubah (repentance) he will never enter into the Jannah. Many of my relatives who died while they had their account in interest (Ribaa) based banks. I wonder what would be their fate. I have asked my parents to shift account to Islamic bank. They have done it partially because of extra facilities and convenience of Ribaa based banks and some business purposes.
Besides there are other major sins to which many Muslims are not aware of and give that much importance like backbiting, severing relationship with kith and kins, etc.
In such cases I am quite anxious about what is likely to be --- will they be punished forever on Hereafter?

All perfect praise be to Allaah, The Lord of the Worlds. I testify that there is none worthy of worship except Allaah, and that Muhammad is His slave and Messenger. We ask Allaah to exalt his mention as well as that of his family and all his companions.

There are evidences from the Book of Allaah, the Sunnah of the Prophet and the consensus of scholars that a person who committed a major sin does not become a non-Muslim, and he will not abide eternally in Hellfire. In case he dies before repenting while believing in the oneness of Allaah, his matter is in the Hands of Allaah. He may, if He so wishes, forgive him and admit him into Paradise without punishing him, and He may, if He so wishes, punish him in the Hellfire and then after punishment He will admit him into Paradise. There are many evidences about this in the Book of Allaah, the Sunnah of the Prophet and the sayings of the righteous predecessors of this nation.

Evidence from the Qur'an:

·         * Allaah says (which means): {Indeed, Allaah does not forgive association with Him, but He forgives what is less than that for whom He wills.}[4:48].

·          * Allaah also says (which means): {And if two factions among the believers should fight, then make settlement between the two. But if one of them oppresses the other, then fight against the one that oppresses until it returns to the ordinance of Allaah. And if it returns, then make settlement between them in justice and act justly. Indeed, Allaah loves those who act justly. The believers are but brothers.}[49:9-19]. It is known that fighting among the believers is a great major sin. Despite this fact, Allaah described them as believers and brothers and did not consider   them as non- Muslims or that they will eternally abide in Hellfire.

·           * Still in another verse Allaah says (which means): {But whoever overlooks from his brother [i.e. the killer] anything, and then there should be a suitable follow-up and payment to him [i.e. the deceased’s heir or legal representative] with good conduct.}[2:178]. In this verse Allaah called the killer a brother of the killed.

Evidence from the Sunnah:

·           * The Prophet said: "Jibreel (Gabriel) came to me and gave me glad tidings that whoever dies from my nation while having not associated anything or anyone with Allaah, will enter Paradise." Abu Tharr asked: 'Even if he has committed adultery or fornication or has stolen?'. The Prophet replied: "Yes, even if he has committed adultery or fornication or has stolen." [Al-Bukhari and Muslim].

·          * The Prophet said: "My intercession is for the people from my nation who had committed great major sins." [Abu Daawood, At-Tirmithi and Ibn Habaan] This is an evidence that the Prophet will intercede on the Day of Judgement for the people who had committed great major sins. If these people are considered as non-Muslims [because of major sins] and will abide eternally in Hellfire, the Prophet would not intercede for them. In relation to the non-Muslims who will eternally abide in Hellfire, Allaah says (which means): {So there will not benefit them the intercession of [any] intercessors.}[74:48].

·          * The Prophet used to punish the people who had committed major sins, yet ask forgiveness for them and pray funeral prayer on whomever died amongst them. Were they considered as non-Muslims who will eternally abide in Hellfire, he would not have done so. Therefore, saying that whoever dies while having committed a great major sin and insisted on committing it will be in the Hellfire forever is wrong; it is only the innovators who said this.

Finally, we advise you to read books about the correct creed as they elaborated on this issue, like the book titled Al-'Aqeedah At-Tahaawiyyh written by Abu Ja'far At-Tahaawi. This book was explained by Imaam Ibn Abu Al-'Iz Al-Hanafi. We are sure that you will find in it convincing answers to your questions.

Allaah knows best.