Sorry to hear you're having trouble! Some follow up questions:
1. Do you see this in all RStudio projects, or only in specific ones?
2. Each project has a (hidden) folder called `.Rproj.user`. If you temporarily move that folder out of the way (e.g. `mv .Rproj.user .Rproj.user.backup from the terminal in that project folder) and re-open RStudio within that project, are you then able to close it?
3. RStudio also stores session state within the `~/.rstudio-desktop` folder. If you move that folder out of the way temporarily (e.g. with `mv ~/.rstudio-desktop ~/.rstudio-desktop-backup`), are you able to successfully close the IDE?
4. Do you only see this when attempting to close a project (ie, explicitly clicking 'Close Project' from the project menu)? Are you able to successfully quit / close the IDE in those projects otherwise?
5. What version of R are you using -- a CRAN binary, or an installation of R retrieved elsewhere?
Any more information you can provide will be helpful here.
Finally, by any chance would you be able to share the project folder wherein the IDE fails to close? If so, can you e-mail a tarball / zipfile to me at kevin <at> rstudio <dot> com? Note that RStudio maintains autosaved backups of files you are editing, so you may not want to share projects containing confidential information.