The poem "Sohrab and Rustum" is part of the Persian epic of Shahnameh.
However, the poems don't provide explicit reasons for why Rustum is not able to live with his wife for a long time. Despite this, we can still make some educated guesses by reading between the lines.
In Shahnameh, Rustum is hunting near the city of Samangan when he loses his beloved horse, Rakhsh. Accordingly, Rakhsh is stolen by some Turanian knights. For his part, Rustum is devastated by the loss of his prized steed. Meanwhile, the Samangan king invites Rustum to stay the night at his palace. The king tells Rustum that he can resume his search in the morning.
During the night hours, the king's daughter, Tahmina, approaches Rustum. She tells him that she has long admired him for his exploits. After all, Rustum is greatly feared by other warriors. Tahmina then offers herself in marriage to Rustum and promises him that she will lay all of Samangan at his feet. As for Rustum, he accepts Princess Tahmina's generous proposition.
The next morning, Rustum's steed is returned to him. After bidding Tahmina a sad farewell, Rustum returns to his country. Shahnameh tells us that Tahmina gives birth to a son nine months after Rustum's departure. She names the baby boy Sohrab. This is the same Sohrab that Rustum unwittingly kills in the poem "Sohrab and Rustum."
From the epic poem Shahnameh, we learn that Rustum is a great warrior. He has battled armies in every land and performed legendary feats. So, part of the reason Rustum is not able to live with Tahmina for a time is because he had to return to his own country, Zabulistan. There, Rustum is a paladin or holy warrior. So, Rustum had responsibilities to his own king and country: this is why he had to return to Zabulistan.
Also, the poem "Sohrab and Rustum" hints at another reason Rustum did not live with Tahmina for a time. In the poem, it is revealed that Tahmina lied about the sex of her child. She sent word to Rustum that she had borne a girl. She lied because she feared that Rustum would raise any boy child of his as a warrior. So, Rustum did not return to Tahmina for a time because he believed that he had a daughter, one who could not be raised as a warrior.