I had the same problem...and I eventually solved it by replacing the connector and the lamp socket.

It begins with a small amount of corrosion. As n0v8or pointed out to me, corrosion causes increased resistance which in turn causes heat. As the situation worsens, the corrosion breaks contact (often restored by wiggling the socket). At some point, the heat actually begins to melt the connector....and the lamp socket. This is what happened in my case.

You can ring this up as another component-level light-socket volvo-ism.

If you buy new connectors, you'll also have to order the wire with female connector ends. These snap into slots in the gray connector body. In my case, my indy shop pulled intact connectors from his used parts inventory. I bought new lamp sockets at a Volvo dealer. (Since both socket and connector warped together, they'd fit each other. But they wouldn't fit onto perfectly shaped replacement parts.)

Before connecting, I sprayed the connections with tri-flow and applied a little dielectric grease (these steps to repel moisture). Then I wrapped the connection with electrical tape - another moisture barrier.
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(98 S70 T5SE misc mods, mostly lighting) (92 940GLE)