Getting stuck opening projects happens for a variety of reasons. If there is one particular project that seems to be stuck on the "Opening Project" screen using the project relaunch button can often times resolve the issue.
There is another bug that we are tracking that results in trouble opening multiple projects. We believe it has to do with an authentication cookie getting lost or deleted at some point while logged into rstudio.cloud. In that case logging out and logging back in will generally resolve the issue.
Sean