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, sallallaahu ʻalayhi wa sallam, is His slave and Messenger.
Brotherhood among Muslims is one of the prerequisites of faith; Allaah, The Exalted, says (what means): {The believers are but brothers...} [Quran 49:10] It is commendable that Muslims maintain good relations and communication that is founded on goodness and good speech. It is also an opportunity to carry out righteous deeds drawing one closer to Allaah and earn great rewards. Ibn ʻUmar said, “We used to go out in the morning only for the sake of the greeting; we would greet whomever we meet.” [Maalik in Al-Muwatta’ and Al-Bukhari in Al-Adab Al-Mufrad]
Moreover, ʻAmr ibn ʻAbasah reported that the Prophet, sallallaahu ʻalayhi wa sallam, said: “To the right of Ar-Rahmaan, and His both Hands are right, there shall be people among the servants of Allaah who are neither Prophets nor martyrs, yet both the Prophets and martyrs will envy them on the Day of Resurrection for their white faces and their rank from Allaah, The Exalted.” They (the people) asked: “Tell us, Messenger of Allaah, who are they?” He, sallallaahu ʻalayhi wa sallam, replied: “They are people having no mutual kinship and property bonding them together; they gather to remember Allaah. They carefully pick their words like the one eating dates would pick the best dates ...” [At-Tabaraani - Al-Albaani graded it Hasan (good) in Saheeh At-Targheeb wa At-Tarheeb]
Communication among Muslims, even if originally founded on a good and righteous basis, may preoccupy the person from doing what is more important and brings about greater benefits. Therefore, moderation is the key factor in this regard. As for the communication that is founded on the disobedience of Allaah, it must be avoided because it incurs nothing but evil.
The realization of benefit is the key factor in deciding whether or not to keep in touch and maintain communication with others. It differs from one person to another and from one situation to the other.
Finally, the hadeeth to which you referred in the question indicating the prohibition of forsaking one’s fellow Muslim more than three days actually refers to the total severance of relations with fellow Muslims and has nothing to do with the topic being discussed in this fatwa. For more benefit, please refer to fataawa 84976 and 86090.
Allaah Knows best.