Why does my SQL Server Express (2014) connection break after restarting my computer?
The problem is very likely related to your machine; not SQL Server 2014 itself.

A few things I would start checking when the same issue happens:


SQL Server Error Log
Windows Event Log
SQL Server Service Account state and password (is the account disabled or locked?)
Try pinging the IP of SQL Server
Try connecting by forcing TCP, using tcp:192.168.0.1,1433 (replace 192.168.0.1 with the actual IP address) 
Try running SysInternal's Process Monitor to see what is happening exactly while attempting the login process.
Is the Kerberos SPN set correctly?


I very much doubt the SQL Server team would release buggy products which even starts failing at login.  The logs will definitely give a clue about what is happening, perhaps the installation logs also show something relevant.