Ghosts hang around until they're exorcised, or get bored and look for some place else to haunt. Ghost ads — the ancient signs for bygone products, painted in the early half of the previous century — linger until the wrecking ball knocks down their brick canvases, or another building goes up and covers them up.
Three old downtown signs are currently in peril.

The Railroad office sign on the side of the Lumber Exchange. For decades the faded, feeble letters CHICAGO ST. LOUIS office could be seen if you decided to look up and the light was right. The sign was covered for decades when the Andrews Hotel doubled its height in the '20s, and it was revealed again when the Andrews thundered down to rubble in 1984. Now the AC Hotel is rising on the site, and while it won't be as tall as the Andrews, it'll make it difficult to see the ghost sign from 4th Street.
The AC building will also cover up downtown's strangest ghost. In between the Lumber Exchange and the Andrews stood a tiny two-story building. It housed a pool hall in a 1912 photo. No idea when it went down. This is the exterior wall of the Lumber Exchange where the building used to stand:

Either someone painted an ad in the alleyway created by the building's demise — which seems as likely as putting it on the roof pointing up, hoping it'll be seen by passing zeppelins — or the sign was for … well, I've no idea. It's not street art. It's not a recognizable ad of any kind. It's always been like this. In a few months it'll be covered up for good, its mystery unsolved.
Also due to vanish: the Sexton Building's ad for … the Sexton Building. It's on Portland and 8th.

Before the building's conversion into housing, the Sexton was a typical old, drafty commercial structure. Offices, light manufacturing, warehouse space and mice. An unglamorous block with some colorful ground-floor retail. Like many structures of the era, it doesn't really look like it wants to be housing, but it beats the alternative.
Last decade there were plans to build an annex on an adjacent parking lot, but the Great Recession kiboshed that idea. To the surprise of casual observers, ground was broken last year, and the parking ramp for the new building — now called the Portland Tower, because it's a Tower on Portland — is almost done.