'Remain' in the Bible

the king told them, "I have dreamed a dream and I will remain troubled until I can understand it."

Just as you saw iron mixed with clay, so they will mix themselves with human offspring. Furthermore, they won't remain together, just as iron doesn't mix with clay.

And whereas it was commanded to leave the stump of the roots of the tree; thy kingdom shall remain unto thee, after that thou shalt know that the heavens do rule.

After a number of years, they'll become allies and the daughter of the southern king will go to the northern king in order to craft alliances. But she won't remain in power, nor will he retain his power. Instead, she'll be surrendered, along with her entourage, the one who fathered her, and the one who supported her at that time.