Losing Wifi Signal Intermittently Constantly

I've been having a problem with my wifi connection.I give my neighbor $15 a month to use his connection, so I have no control over the router.I'll be surfing along or just checking mail or whatever and out of the blue my connection stops. A little yellow triangle "warning" sign covers the signal strength meter in the lower right corner. If I click on the signal meter, up pops the list of wireless connections available to me and says that I'm connected, (but I'm not). So I go to the network and sharing center and sometimes this alone will restart the signal but usually I have to run the troubleshooter and the signal will come back with no explanation of what the problem is.While in the network and sharing center, my connection to the router looks clear and connected but shows a red X over the connection between the router and Internet.