Do you want to fix this on the frontend (e.g. restrict the users to login twice) or on the backend (e.g. discouple your backend implementation & cache from HTTP sessions.
With users getting more and more mobile, I feel that you should rather go and fix the backend problem and adapt your architecture accordingly.
I know that this doesn't exactly answer your questions, but I feel this is quite a critical aspect of a software architecture. In 95% of apps where I've seen this demand, it was not for business reasons (where this actually makes sense) but rather as a technical workaround.