Question:

In the time of exile, G-d "hides His face" from us. Does this mean that there is no Divine providence during this time? 

Answer:

In last week's Torah portion (Vayelech, 31:17), we read the verse, "...And I will hide My face from them, and they will be consumed, and many evils and troubles will befall them, and they will say on that day, 'Is it not because our God is no longer among us, that these evils have befallen us?'" Maimonides explains that as a result of G-d's "hiding His face," the Jewish people will appear to have been abandoned to the forces of nature, and as a result, troubles will befall them.

These events can lead us to err and think that there no longer is any direct Divine providence in the time of exile, and all events transpire by coincidence. However, the truth is that the removal of Divine protection mentioned by Maimonides refers only to the removal of G-d's revealed protection. G-d continues to direct all events in a hidden way, even in the time of exile.

If we examine the above verse in the Torah carefully, it states, "And I will hide My face," but not "I will remove My face," G-d forbid. G-d only hides His direct protection, but never completely removes His presence. The seeming lack of Divine protection leads us to think that G-d is not in our midst, G-d forbid. However, as Maimonides writes, it is forbidden to say on troubles that have befallen a person that it is "the nature of the world," or a "coincidence." All is a result of Divine providence.

So is written in the book Shomer Emunim: "There is nothing that happens by coincidence, without direct Divine providence, as is written, 'I will walk among you by happenstance.' Even when events seem to be by happenstance, they are all attributed to Him, and are all by His Divine providence."

However, with the coming of the true Redemption, the concealment will be removed and the truth will be revealed, that G-d's presence was with us the entire time. 

Sources: Moreh Nevuchim Part I, chapter 23, and Part III, chapter 51. Mishneh Torah, Hilchot Taaniyot, 1:3. Shomer Emunim, end. Likutei Sichot vol. 18, p. 199.