This video tribute says more than I could, but I'll cut to the chase: closed in 1972, and demolished shortly thereafter.

A 1949 discussion about the rights of Negro Nurses:

. . . . the young graduates of Negro schools take the examinations with the white nurses and some of those examinations are held at the Robert E. Lee Hotel in Winston-Salem, one of the best hotels in the state. The hotel permits those girls to go into the front door, to stand in line and they do not stay there but they go right in the front door as any other person would do and I think that shows that generally speaking a lot of progress has been made in this respect.

In case you were wondering, which any sensible person would. Other hotels made the educators come in the back way, or, if they used the front door, they had to move quickly through the lobby.