There may be corrosion (increased resistance) in a connection somewhere. Since headlights draw a reasonable amount of current, that may mean that connection is getting hot, and may fail soon. This may be why you've had to replace sockets. If so, I'd look for the reason and fix that. Is a liner or cover missing, allowing water and dirt into the socket?
I'd check wire splices and ground points. A volt-ohm meter and wiring diagram would be needed for this. A non-contact IR thermometer may help, too.
My wiring diagram does not show any obvious common connections between the high and low beam circuits, so I don't see an obvious place to start.
And I have to ask the obvious--is the headlight lens clean? And have you tried changing bulbs from side to side?