The justification for login timeouts depends on the security level of your application and the how the users use the app. If your app handles financial/sensitive data, the login timeout should be short (logically), approx. 3-5 minutes.
If your app is a CMS, use a longer timeout. I would suggest approx. 45-60 minutes. This is to prevent content administrators from loosing content or content formatting if they are on the WYSIWYG editor screen for 30 minutes, which I frequently see.
In regards to justification for no timeout at all; I have one site that has a no login timeout. It is specifically for sales reps that always forget their passwords. This was a required feature by the client, not my normal best practice. Everyone has their specific needs and business objectives.
My strongest recommendation here is, know the audience. Make sure you understand what the users are doing and how long they are one a page on your site before setting up a login timeout.