DNS resolution broken in El Capitan with Thunderbolt Ethernet Adapter on Offline network
I had the same problem on El Capitan, and was able to resolve it by adding some values to the DNSResponder file, while SIP was DISABLED.

The steps I followed below:


Reboot.
Press Cmd+R to enter Recovery mode.
Open Utilities->Terminal.
Run the command "csrutil disable".
Reboot. You are back in OS X with SIP disabled.
Make the required changes by running the below commands from the terminal:


sudo launchctl unload /System/Library/LaunchDaemons/com.apple.mDNSResponder.plist

sudo defaults write /Library/Preferences/com.apple.mDNSResponder.plist AlwaysAppendSearchDomains -bool YES
(This is a single line)

sudo launchctl load /System/Library/LaunchDaemons/com.apple.mDNSResponder.plist


Reboot.
Press Cmd+R to enter Recovery mode.
Open Utilities->Terminal.
Run the command csrutil enable.
Reboot.


After I got back into the OS, I added the search domains back into System Pref -> Network -> Advanced -> DNS Tab.  

Search Domains now work once again, where I am able to ping the first two bits of my domain name, and the last 3 are added automatically.