Rosie,
I bet you dollars to donuts that you have a defective socket or two. I have recently run into several sockets that were defective. If you don't have to seriously push on the bulb to get it to go into the locked position or can't get it there at all, that is what you have.
There is supposed to be a slot or a forming that causes the pins of the bulb to lock into the bayonet. This feature is a kind of L shape with the short part towards the lens. If this is the case, and it does not cause the bulb to lock in, it can be repaired buying a replacement socket is the better bet.
Some years back, I ran into sockets that did not have springs, but had rubber plugs for the contact base and the rubber aged out. If that is what you have, just cut the effort and go buy new sockets.
Matt