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In the generally-accepted reading, this phrase is spelled li-mustagarrin laha, which may be rendered as above or, more conventionally, as "to its point of rest", i.e., the time (or point) of the daily sunset (Razi). However, Abd Allah ibn Masud is reliably reported to have read these words as la mustaqarra laha (Zamakhshari), which gives us the meaning of "it runs [on its course] without having any rest", i.e., unceasingly.
Mustaqarr may mean: (1) a limit of time, a period determined, as in vi. 67, or (2) a place of rest or quiescence; or (3) a dwelling place, as in ii. 36. I think the first meaning is best applicable here; but some Commentators take the second meaning. In that case the simile would be that of the sun running a race while he is visible to us, and taking a rest during the night to prepare himself to renew his race the following day. His stay with the antipodes appears to us as his period of rest.