diff --git a/changes/2647.misc.rst b/changes/2647.misc.rst
new file mode 100644
index 0000000000..53f125b265
--- /dev/null
+++ b/changes/2647.misc.rst
@@ -0,0 +1 @@
+The "live docs" tox environments were updated to allow a grace period for ``sphinx-autobuild`` to shutdown the HTTP server. Without waiting, the HTTP server may have been left running when tox exited.
diff --git a/tox.ini b/tox.ini
index 271f8bbabd..00152d87f8 100644
--- a/tox.ini
+++ b/tox.ini
@@ -93,6 +93,8 @@ sphinx_args = -T -W --keep-going --jobs auto
 
 [testenv:docs{,-lint,-all,-live,-live-src}]
 skip_install = True
+# give sphinx-autobuild time to shutdown http server
+suicide_timeout = 1
 deps =
     # editable install so docstrings can be updated for 'all' and 'live'
     -e {tox_root}{/}core[docs]