My LHBS is surviving, but mainly because it is also a cidery and wine maker with a small bar and tables - the homebrew section is probably a quarter of the whole place, but they are great about ordering anything special and it comes within a week, typically. I patronize it to keep it going and because it is pretty convenient - a 20 minute drive from my house. The staff are award winning homebrewers turned into commercial cider and wine makers and their taps rotate with local brewpubs' beers and hard to get foreign beers, so stopping for a beer while picking up homebrew supplies is a real treat.
I sure hope that it stays in business. Homebrewers are notoriously cheap (me included), but having a local specialty store justifies some extra support beyond seeking the absolute best pricing available, unless you are willing to buy online exclusively. So on this issue, I support the local business.