I have the exact same issue with my '93. Through my research, I've found that if the relay gets "stuck" open, supposedly it can route too much power to the door locks and burn out the solenoids. Apparently Volvo fixed this issue later by fitting better lock motors with a resistor in them to avoid the problem. Somewhere on the web (I think it might have been here, in fact) I had read an article showing how to replace just the motors in the existing locks with a better unit.

And before anyone asks, yes, I've replaced my relay with no luck.

It looks like my solution is to replace the four dead locks (one on the rear passenger side still works - go figure). Which is not only expensive, but a big PITA to do yourself. Either that or do what I've done the last year - use the key.

If anyone has a better idea, please, let me know - I'd love to find an easier way.