Scrobbling from Web App without keeping users password

Is it possible to let my users scrobble via my Web App without keeping their passwords in clear-text in my database (which would be bad of course) . I see how this is okay in local clients though.

I understand how to get the authorization token, but it is only valid for 60 minutes and my users probably don't want to authorize my app every time they use my service.

So, first of all, is this possible?
And if it is, what method should I use?

Thanks!