I'm having an issue with a 3-way switch that I have not gotten around to fixing in many years. When I use switch A to turn on the light and then use switch B to try to turn it off, it flickers off and then back on. When I use switch B to turn on the light and then use switch A to try to turn it off, nothing happens. Any advice on what is causing this would be much appreciated.
Replace switch B. Sounds like something broke inside the switch.
Start out by checking the connections on switch B, especially the travelers which hopefully will be marked in yellow. If all is good, replace the switch. Since you've been having the problem for years, replace both switches, they are pretty inexpensive. Take a picture of the back of the switches before unhooking any wires. There is no standard for the connections and the new switches might not be the same as the old ones. Good luck