When a branch is reintegrated to the trunk, is that branch effectively dead?
Can you make modifications to the branch after the reintegration and merge those back
First of all, you should upgrade your Subversion client and server if you still use Subversion 1.7 or older. There is no reason to be using very old Subversion releases. As of 2016, the current version is Subversion 1.9. SVN 1.8 is also supported now and still receives bug fixes.
The problem you ask about was solved in Subversion 1.8. Beginning with SVN 1.8, --reintegrate option has been deprecated. Reintegrate merges are now performed automatically. See Subversion 1.8 Release Notes entry related to the improvement.
Read SVNBook 1.8 | Reintegrating a branch:
If you choose not to delete your branch after reintegrating it to the trunk you may continue to perform sync merges from the trunk and then reintegrate the branch again. If you do this, only the changes made on your branch after the first reintegrate are merged to the trunk.
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Only Subversion 1.8 supports this reuse of a feature branch. Earlier versions require some special handling before a feature branch can be reintegrated more than once. See the earlier version of this chapter for more information: http://svnbook.red-bean.com/en/1.7/svn.branchmerge.basicmerging.html#svn.branchemerge.basicmerging.reintegrate