Ah, we have struggled with this problem in the last month or two. We are with Virgin and my Kindle, which had worked very well for the last couple of years, suddenly stopped connecting to our wifi.
I bought another Kindle thinking mine had had its day but the new Paperwhite would not connect either.
Research on the net showed this is a problem experienced by many people, especially those who have been given the new Virgin superhub.
After much phoning of the Virgin helpline we now have connection for both the Kindles.