There's a well know bug in Google Chrome that forces you to use the same Google Account (let's name it account A) both in Google Chrome and in all Google apps that you have run in this browser. Logging-off this account in any of Google apps causes immediate log-off in Google Chrome as well and also causes your Google data synchronisation to stop.
This may be obvious and convenient in most cases, but fails completely in certain scenarios.
For example, I am using Google Chrome in my office and I am syncing all Google data to a separate account B (to have i.e. separate set of bookmarks, for my work only and to not mix them up with my private bookmarks), but when opening Gmail, I want to be logged in to account A (private one), because I'm checking my private e-mails this way (I am using Outlook for office e-mails).
There's a workaround for this problem ("best answer" here). However, it turned out to be not working for me.