I am using a floating license server for my licenses.
In Vivado 2017.3 I can no longer check out licenses, even though I was able to do this in older versions.
Vivado 2017.3 now uses FlexLM 18.104.22.168, which older floating server machines cannot provide licenses to unless the license utilities version matches or is newer.
Floating license users must upgrade their license utilities in order for licenses to be picked up in Vivado 2017.3.
You can obtain these utilities on the downloads page (https://www.xilinx.com/support/download.html).
Note: The 22.214.171.124 license utilities require that the machine have the 2015 Microsoft Redistributables installed before running (this is already included if Vivado 2017.3 is installed).
See (Xilinx Answer 69504) for further details.