Skype logs out with 401 error if Office 365 is logged out on same browser

[Senjuti]

I am logged in to Skype for Businesson my AngularJS application, through Microsoft Outlook account, and am facing the issue that if I open Office 365 in a new browser, log out of my Microsoft Outlook account account and then refresh my AngularJS application, Skype will have logged out on my application. Is there any possible fix for this?

Console displays 401 error:
GET https://webdirca1.online.lync.com/Autodiscover/AutodiscoverService.svc/root/oauth/user 401 (Unauthorized)