Q. As a divorced woman do I need to cover my hair: when at Shul, in public, all the time?
A. Shulchan Oruch (E.H. 21, 2) rules that Jewish women should not go out with uncovered hair to public places, regardless if married or not. Perisha, Bais Shmuel, Beer Heitev, (ibid. 3 and 5) and others explain that "unmarried" refers to a widow or a divorced woman.
Igrois Moishe (E.H. 1,57 and 4,32,4) rules that in cases of severe economic need, (as the loss of ones job due to keeping this mitzvah) the above-mentioned women are not obligated to comply with the mitzvah of covering their hair. He adds that the same applies when this is a factor in assisting them to remarry.
However, many contemporary Poskim disagree, as they see this as a prohibition and not only a mitzvah (Yesodos Habais Ukedushoso p. 80 - Meir Oz 75,2,10). Some argue that the quality hairpieces available today hardly create hardship.
Horav Shlomo Miller's Shlit"a opinion is indeed to be stringent.
Rabbi A. Bartfeld as revised by Horav Shlomo Miller Shlit"a