Router & Firewall

First check if port 26000 and/or 3724 are open and unrestricted
If there are any packet scheduling enabled, it has caused problems in many cases.
If DMZ ( Demilitarized Zone ) is in effect and if the computer playing the game has DMZ set to it's IP in the router.
In some cases disabling DMZ has solved connection issues.
If there are any program restrictions set, if so disable those.
Sometimes it's needed to disable the firewall completely in order to connect. Do note that some firewalls do not disable themselves completely, unless they are removed from the Windows startup process and the computer rebooted.
Check your DHCP settings, it's possible your router is configured to update the IP address every X hours
If you have any kind of Network software configuration try disabling it or reconfiguring it( i.e. the nVidia Network package has caused problems under some circumstances)
If you use any kind of Parental software such as NetNanny make sure that it's configured correctly by adding eve.exe and exefile.exe to it's exception list
If you are connecting through VPN and can not connect or are suffering disconnections of any kind, try disconnecting the VPN to see if there's any difference.
If all goes well then you might need to reconfigure your settings in your router or VPN software so it does not route the traffic to Tranquility through the VPN connection.

What protocol and ports does Dota 2 use?
Dota 2 uses the UDP protocol and communicates on ports 27015 through 28999 to our dedicated servers. By default, your client opens UDP port 27005 or your computer to connect to the game servers