I have a project with a connection that was working properly on the same device. I suddenly got the error below. And I could connect from the same device through MySQL workbench
I was able to fix this issue on my PC using R 3.4 by following @Page's advice to look into the package versioning. However, not only did I need to install an earlier version of RMySQL (reverting from 0.10.11 to 0.10.9), I also needed to change versions on its dependancy package DBI (reverting from 0.6-1 to 0.5), using the following command:
require(devtools)
install_version("DBI", version = "0.5", repos = "http://cran.us.r-project.org")
install_version("RMySQL", version = "0.10.9", repos = "http://cran.us.r-project.org")