From my experience with this same phenomenon, my guess is that when you pull a G4 bi pin lamp out of the socket, from which, it was not working, you will see that the pins are often darkened. This, I'm thinking, is carbon build up, a result of the arcing that takes place because the contact area is small, and if the tension on the springs of the contacts within the socket, are weak. This arcing and subsequent carbon build up actually insulates the pins from making the electrical connection with the socket contacts.
If you take the lamp out and run the pins along an emery board or a small piece of sand paper, you can shine the pins up and the lamp will work.... for a little while.
I used to have this problem a few years ago with Coppermoons path lights as they used G4 bi pins.. but now, since they switched to G 6.53 bi pins, there is no more problem.
So besides contact grease, I would get a good quality electrical contact cleaner and spray that into the socket holes with the little plastic tube ( a la WD40) and that should buy you some more time.
IF the socket in the fixture you are using will accept a G 6.53 lamp, then use it, but be cautioned that once you do, you can't go back to a G4... the problem will only be worsened.