RS ASIO will try to request 48kHz mode, but your drivers may or may not allow this, so it might help setting it manually. You can find local folder of a game by right clicking on a Rocksmith in your Steam library, and selecting menu 'Manage' -> 'Browse local files'
Copy the contents ( avrt.dll, RS_ASIO.dll, RS_ASIO.ini) of latest release (zip archive release-xxx.zip) to the game folder.It patches game code at runtime to allow intervening in the process of WASAPI device enumeration so that we can inject our own fake WASAPI devices which internally use ASIO audio API. This project aims to add ASIO support to Rocksmith 2014 Edition - Remastered in order to avoid issues with some WASAPI drivers.