Must Login to all accounts upon PC restart

> Everytime I reboot my computer, I have to re login into every site on
> Chrome.

   When you shut down the computer, all its network connections are
lost.  When you start it again, you must establish them again.

> Is there a setting that I need to change on my router to avoid this?

   No.  So far as I know, there's no setting on _anything_ which would
change that.

   You should be able to have your web browser save credentials (user
names, passwords, ...) for the sites you visit, but that may or may not
be enough to let it restore everything as it was before.  The router
certainly can't help.

The router should not impact web sessions. If you are not staying logged into websites, then it means that you likely have chrome set to not save cookies, or to clear history on exit.