Radak explains similar to what has been already mentioned that ינום - slumbers derives from the word 'תנומה' which is a light sleep/doze and is less than שינה - sleep.1 Thus emphasising, that come what may, Hashem does not doze or sleep when He guards Israel at all times, He is completely committed to looking after His people.
Alternatively, Malbim writes as follows:
הנה לא ינום, שלא ינום מחמת לאות וחולשה, ויותר מזה כי לא יישן כלל כי לא נמצא אצלו טבע השינה כלל, שבן אדם אף מי שלא ינום מחמת עיפות הלא מוכרח הוא לישן ולהעמיד אז שומר אחר תחתיו:
Behold He neither slumbers - He does not slumber as a result of fatigue and weakness, and more than this He will not sleep at all because we don't find that he He has the nature of sleep at all. A human even if he does not doze as a result of tiredness he is still forced to sleep and they then put another guard instead of him.
So Malbim explains that Hashem who constantly guards Israel does not slumber due to fatigue and the like, and nor does He sleep naturally. Rather He is always there watching over us and never needs replacing like that of a human guard. (See also Malbim and his comment on Yeshaya 5:27 where the same words are used).
1 In Yevamos 54a it helps to provide a clear definition of this word ינום. It writes there:
ה"ד מתנמנם אמר רב אשי נים ולא נים תיר ולא תיר כגון דקרו ליה ועני ולא ידע לאהדורי סברא וכי מדכרו ליה מדכר
What are the circumstances of dozing? Rav Ashi said: One is asleep but not asleep, awake but not awake, when, if they call him, he will answer, but he is unable to provide a reasonable answer. And when they later inform him of what happened, he remembers it. (Sefaria translation & notation)