After packrat::init(), what does the packrat/* folder look like? The packrat.lock file, etc.? One issue you may be having is that packrat is not "on." packrat::on() is the solution here, and should work if your current working directory is in the project directory.
The other way you can check to see if packrat has done its "magic" is to look at .libPaths(). If packrat is "on," then your libpaths should point to the packrat/* folders for packages.
One final way is by sourcing the packrat/init.R file with source("packrat/init.R") (which is added to your .Rprofile by default).
I'm curious to hear about the state of your directory when you experience this problem!