I think you are misunderstanding how authentication works with ASP.Net. As an example, let me show you some cookie details for a site of mine that uses Identity (note the token is actually in the cookie, the two are not mutually exclusive concepts):
Name __RequestVerificationToken
Value afeILhaIvRr56jXXXXXXXXXXX
Host site.azurewebsites.net
Path /
Expires At end of session
Note that the cookie, by default, expires at the end of your session. That means when you restart your development machine, your cookie is expired and your token is no longer valid.
In particular I have read that with token authentication then there is no need for continual re-authentication every time a request is made to the server
You need to understand that HTTP is a stateless protocol. Each request happens in a vacuum, and therefore you need to pass some data back to the server so that it can tell that the person who authenticated with Request A is really the initiator of Request B. Almost always, that piece of data is from a cookie. So, every request does indeed re-authenticate, and typically with a token in a cookie.
The only piece of data about your session that is stored on the client is the cookie (unless you are doing something atypical). The rest is on the server. How it is stored can vary:
Inproc: Easiest to setup, sessions are stored in process. So when your server or app pool is restarted, that data disappears
State Server Mode: Sessions are stored in process, but outside of the ASP.Net worker process, so the application can be restarted without losing session data
SQL Server: Unsurprisingly, this stores data in a database. Very resilient, but more work to setup. Also your best option if you are on a web farm.
ref: http://msdn.microsoft.com/en-us/library/vstudio/ms178586(v=vs.100).aspx