Can you also try taking a look at the request log, and checking out what the failed requests look like? You can do this by pressing Ctrl + ` in the IDE. You should see a number of horizontal lines; each line represents the time between a request and a response sent from the RStudio desktop to the running R session. By clicking one of those lines, you should (hopefully) get a bit more information as to why you're getting these 400 errors.
Unfortunately, it's hard to say what could be causing this.