Well this could be down to a security update from windows - I assume her PC has XP autoupdates on (ah, also assuming XP is the OS), so one that has downloaded in the background might be limiting access to the webmail. You could try going to internet options and in privacy changing the security settings to medium.
In terms of getting e-mail, why not used outlook express (but make sure e-mails are kept on teh server - there's a selection box for this), or even mozilla thunderbird? That way the e-mails can be saved to the HDD as well. Of course, you'd need to get the IMAP settings (or POP3 if they do it) for the webmail host.