I'll support my LBS whenever possible, but not at any price. And by that I don't mean how much they charge, but how they treat the customers. I'm fortunate enough to live close to a major city with plenty of choice. Some of the LBS are great, others not so much.
I used to frequent one in particular, but will never set foot in there again after the condescending way the staff treated a female friend who went there on my recommendation. After that, I visited another store and was bowled over by their friendliness and the level of service they offered. They get my business now.
In contrast, I grew up in a small town with only one bike shop. The Internet didn't exist then and going to another town wasn't an option. That store had you by the short and curlies and they knew it. I was only 11 or 12 when I first got into cycling and had to save my weekly allowance to buy bike stuff. I loved my bike but dreaded having to go into that store and deal with the smug, know-it-all staff who's idea of a great joke was to send me out the door with the wrong part and then give me crap when I tried to exchange it. The manager was the worst of the bunch.
Eventually, someone opened a new store and the original place went out of business in 6 months. The guy who managed the original store tried to get a job at the new place and the owner told him if he ever set foot on the premises again, it would be the last thing he did.
The advent of both the Internet and big box stores has changed the way 'all' retailers do business. It's a different world today than it was 20 or 30 years ago. But there's still room for stores offering a level of service and support which can't be found online or at Home Depot. Not all will survive but for the most part, the good ones will.