This is not an Eclipse issue, but a SVN issue.
If you could see your repo in a web browser, the SVN FAQ mentions an httpd.conf error. But in your case:
I then created a subdirectory "projectx" under ~/webapps/svn with subdirectories "trunk", "branches" etc and then ran:
$ svn import projectx file:///home/<user>/webapps/svn/projectx -m "first import".
projectx/trunk etc showed up fine on Trac, and https://svn.<user>.webfactional.com/projectx/ showed up fine in the browser, with proper authentication etc. All well and good.
However, when attempting to check out the project from trunk (using Tortoise SVN), I got this error:
Command: Checkout from https://svn.<user>.webfactional.com/projectx/trunk, revision HEAD, Fully recursive, Externals included
Error: Repository moved permanently to
Error: 'http://svn.<user>.webfactional.com/projectx/trunk/'; please relocate
With the solution being:
You've created directories on the filesystem below your repo, eg ~/webapps/svn/projectx. That's the wrong way.
You should instead use 'svn mkdir' to create the directories.
If this is not enough, see also this SO question, where it mentions that the repository address is usually http://servername/svn/repositoryname, not http://servername/svn.