It is the act of bringing near.
Imam Abū Bakr Fūrek said: The letter "sīn" in the word istiqāma (uprightness) signifies the meaning of seeking. That is, the Sufis sought from Allah, Glorified and Exalted is He, that He keep them upon their tawhid (the oneness of God), then that He make them constant in their covenants, and that they not transgress the divine limits.
Imam Abū'l-Qāsim Qushayrī said: Istiqāma is a rank by which everything attains its kamāl (perfection) and is completed. The attainment and order of all good things is possible through it. Whoever is not upright in his ḥāl (spiritual state), his himma (spiritual aspiration) is wasted, and his effort is in vain... The sign of istiqāma for the beginners (those at the beginning of the path) is that there is no weariness in their deeds. The sign of istiqāma for those of the intermediates (those who have passed the initial stage and reached the middle of the path) is that there is no stagnation in their maqām (spiritual station). The sign of istiqāma for those of the advanced (the people of the end) is that no veil comes between them and union (wuṣla) with Allah, the Exalted.
One of the Sufis said: A person who possesses istiqāma should not be eager for karāma (a saintly wonder). For the nafs (the lower self) constantly incites the desire to display karāma. However, your Lord does not expect you to display karāma, but to be upon istiqāma.
It has also been said: None but the great ones are able to maintain istiqāma. (Nabhānī, II, 86)