Whenever I tell chess.com to remember me, the next time I try to go to chess.com it tells me that the site is under maintainance and the next time after that, chess.com works but I am not logged on.  This problem has only started to occur recently and I have to made any changes to my internet connection.  Is this problem my fault or is something going on here at chess.com?  And what should I do to stop this from happening apart from not telling chess.com to remember me?

I would recommend deleting all of the temporary internet files (sometimes called cache) that are stored by your browser. If you are unsure how to do this, here is a tutorial: http://support.chess.com/index.php?_m=troubleshooter&_a=steps&troubleshootercatid=1&parentid=0 . 

I just tried that but it still isn't working properly.  Any other suggestions?