I think shopping locally at a LHBS or buying online boils down to a matter of choice, and the choice to shop the LHBS determines if they stay in business or not.
Add to that your LBHS geographic availability....is said store 3 minutes away OR is it 100 miles one way? This makes a difference to me.
Supporting the LHBS keeps open the store so you can run by the afternoon before you brew when you realize you need yeast or a bit of specialty grain. This makes it easy for those who keep small quantities on hand.
On the other hand, LHBS is sometimes more expensive (varies by store and location) since they may deal with smaller volumes than the online suppliers. And online sales companies often have fresh supplies since they tend to move faster than some low volume LHBS.
A home brewer friend turned pro and opened a brewery in a huge warehouse with room to spare. We talked about sectioning off an area to build a LHBS but the overwhelming consensus was that the market would not support this endeavor. Just my opinion, but in my area I think online is winning this battle.