One of the things I hate about Microsoft is the way that they use the same name for two entirely different things. When most people refer to a 'Windows Live Mail account' they mean an email account with what's now Outlook.com. However the information in your post suggests that you're referring to a Gmail account, which you access through the email client which is also, confusingly, known as Windows Live Mail. So I'll proceed on that basis:
Delete your Gmail account from the Windows Live Mail email client. (Don't worry - you won't lose any emails! You're only removing the settings for the account, not actual email content). Then create the account again. That's likely to fix the problem for you.
(BTW: I assume that you only access your mail through your home computer and not through any other device, such as a smartphone. If you use multiple devices you ought to be using an 'IMAP' connection, rather than a 'POP3' one).