Let me put the Ouija Board up before I stop trimming my eyebrows and start being insensitive and cranky.
Now on to my answer.
There are at least two reasons at work in most communities, and they are related. First, putting up signs costs money. When a business operation ceases, the owners of the existing property probably hope to replace it with or sell it to a new business operation. That business will likely want a sign; so taking one down, which isn't free, just to put up another, also not free, is inefficient.
Second, putting up signs costs money--no, I'm not being redundantly repetitive as I restate that again. In the second case I have in mind an artificial cost: a legal permit to put up a sign.
Because high-minded people don't like "ugly" signs that help people navigate to places they'd like to go including places they may not realize they want to go until they see the sign (but I digress), the high-minded people impose limitations on signs and billboards. This has the intended effect of reducing the signs that "blight" our view. The also has the unintended effect of encouraging signs to remain standing even after they don't serve an advertising purpose and are presumably maximizing blight including promoting false information... (Sorry, kids. That wasn't a sign for a Happy, Fun Burger. That was a sign for where a Happy, Fun Burger used to be.)
I had been thinking about this phenomenon recently when I came across this Megan McArdle article on how limiting divorce may limit marriage in an undesirable way. She adeptly points out that limiting exit can limit entry, which means many couples will not take the generally beneficial step of formal marriage.
We can say this about the sign permit effect: If you make signs and billboards difficult to put up, you'll make them difficult to take down as well. The unintended consequence of limiting signs coming up is that they will tend to stick around after their use life negating the purpose of the original limitation. We can generalize this to include things like marriage and employment, another issue McArdle brings up: If you make things artificially difficult, you risk discouraging the good versions and encouraging the bad versions of that thing.
PS. One quibble with a point Megan makes in her last paragraph. She writes, "As conservatives are fond of noting, societies, like economies, are very complex organic systems. We do not understand them, much less control them with a few simple tweaks." I would say conservatives are fond of noting this when it serves their particular purposes. While libertarians recoil at the idea of tweaking society with near-ubiquitous consistency, conservatives are far too tolerant of tweaks in the "right" direction.