I started getting the same thing when I got my Vista (business) laptop. At the office, I have a 3Com wireless access point. At home I have a Netgear WGR614v6.
When I get to the office, I have no trouble getting connected. But when I get home, my PC gets the same "Local" BS too. Normally...I put my computer in sleep mode between the office and home. But it doesn't matter if I turn it off, put it in sleep mode. I still have trouble at home.
Now here's the kicker. When I go out I have no trouble getting on anyother wifi connection.

lol
The only solution I've found that works*, was to write a .bat command.
ipconfig /release
ipconfig /renew
After that I just have to let my PC find the network and once its fails, I just hit my .bat file and within a few seconds (15sec tops).
Hope it helps.