Chrome isn't really suitable for a portable browser. It only has unofficial versions and even the one you're using from portableapps is listing multiple issues with the version:
Passwords Not Saved Between PCs By Default: Google Chrome stores
passwords in such a way that they are encrypted in a way tied to
current PC. While the passwords are not kept or left behind on the PC
itself, they won't be retrievable when you move to a new PC. We've
added password portability as an advanced option, though, which you
can enable by reading the help.html file.
Certificates Not Portable: Google Chrome has no certificate manager.
It uses Windows' certificates manager. So, any certificates you
install through the Google Chrome interface are stored on the current
local machine and will not travel with you. Thus, you should not use
any private certificates with Google Chrome except on your own PC.
Some Settings/Extensions Locked Per PC: Google Chrome locks specific
settings to a given PC. Details are included in this post. This
behavior is by design by the Chrome team. If you would like this
changed, please file a bug with the Chrome team. A suggested
workaround is to sign in to Google to restore all settings and
extensions and to use an extension such as Session Buddy to maintain
your session state as you move PCs. Note that PortableApps.com has not
evaluated this extension.
Note that other portable browsers such as Mozilla Firefox, Portable
Edition do not have any of the issues mentioned above. These issues
are specific to Chrome due to Chrome's design and not something we can
work around without fixes to the base app by the Chrome developers.
That includes a hint for Session Buddy extension to maintain sessions. And I'm sure you're using some older version which likely may have had even more issues with portability, e.g. with mentioned cookies.
I would recommend looking at browsers which have official portable versions instead, they're much more likely to be fully portable. For example Opera. It specifically states that:
No matter which computer you work on, you can always run the Opera browser from a USB drive. Your browsing history, bookmarks, installed extensions and other data will only be saved to your user profile on the USB. None of that info will be stored locally on the computer.
--profile-directory
(peter.sh/experiments/chromium-command-line-switches), but regardless, Chrome isn't the best choice ever for a portable browser, it has never been advertised as such, not even sure if there's an official portable version.