I have a two set phone and both phones will charge on the master.
When I put either phone on the extension charger the light will come
on, but after 1 second it dies out.

I have used a pencil eraser and cleaned the terminals as best as I can
but the charger light will not stay on and it is not charging. The
spring on one side looks a little weaker than the other side, but I am
pretty sure both are making contact.

It is an ATT phone. It is not this model but the base handset looks
like it.
http://att.onlinephonestore.com/deta...s-20-2422.html

I am thinking about taking some WD40, and spray each terminal as a
last ditch attempt to get it to work.