diff --git a/django/db/backends/__init__.py b/django/db/backends/__init__.py
index a8e0cc526c..4a03ccb658 100644
--- a/django/db/backends/__init__.py
+++ b/django/db/backends/__init__.py
@@ -351,9 +351,14 @@ class BaseDatabaseWrapper(object):
     def is_usable(self):
         """
         Tests if the database connection is usable.
+
         This function may assume that self.connection is not None.
+
+        Actual implementations should take care not to raise exceptions
+        as that may prevent Django from recycling unusable connections.
         """
-        raise NotImplementedError('subclasses of BaseDatabaseWrapper may require an is_usable() method')
+        raise NotImplementedError(
+            "subclasses of BaseDatabaseWrapper may require an is_usable() method")
 
     def close_if_unusable_or_obsolete(self):
         """
diff --git a/django/db/backends/mysql/base.py b/django/db/backends/mysql/base.py
index 61a8ab72fc..cbe37fc84c 100644
--- a/django/db/backends/mysql/base.py
+++ b/django/db/backends/mysql/base.py
@@ -552,7 +552,7 @@ class DatabaseWrapper(BaseDatabaseWrapper):
     def is_usable(self):
         try:
             self.connection.ping()
-        except DatabaseError:
+        except Database.Error:
             return False
         else:
             return True
diff --git a/django/db/backends/oracle/base.py b/django/db/backends/oracle/base.py
index 830a8a9862..da0fdb121f 100644
--- a/django/db/backends/oracle/base.py
+++ b/django/db/backends/oracle/base.py
@@ -704,7 +704,7 @@ class DatabaseWrapper(BaseDatabaseWrapper):
             else:
                 # Use a cx_Oracle cursor directly, bypassing Django's utilities.
                 self.connection.cursor().execute("SELECT 1 FROM DUAL")
-        except DatabaseError:
+        except Database.Error:
             return False
         else:
             return True
diff --git a/django/db/backends/postgresql_psycopg2/base.py b/django/db/backends/postgresql_psycopg2/base.py
index dbba3d6d7d..47bcf2f41a 100644
--- a/django/db/backends/postgresql_psycopg2/base.py
+++ b/django/db/backends/postgresql_psycopg2/base.py
@@ -210,7 +210,7 @@ class DatabaseWrapper(BaseDatabaseWrapper):
         try:
             # Use a psycopg cursor directly, bypassing Django's utilities.
             self.connection.cursor().execute("SELECT 1")
-        except DatabaseError:
+        except Database.Error:
             return False
         else:
             return True
diff --git a/tests/backends/tests.py b/tests/backends/tests.py
index ee1e56676f..da851da166 100644
--- a/tests/backends/tests.py
+++ b/tests/backends/tests.py
@@ -665,6 +665,37 @@ class BackendTestCase(TestCase):
         self.assertTrue(cursor.closed)
 
 
+class IsUsableTests(TransactionTestCase):
+    # Avoid using a regular TestCase because Django really dislikes closing
+    # the database connection inside a transaction at this point (#21202).
+
+    available_apps = []
+
+    # Unfortunately with sqlite3 the in-memory test database cannot be closed.
+    @skipUnlessDBFeature('test_db_allows_multiple_connections')
+    def test_is_usable_after_database_disconnects(self):
+        """
+        Test that is_usable() doesn't crash when the database disconnects.
+
+        Regression for #21553.
+        """
+        # Open a connection to the database.
+        with connection.cursor():
+            pass
+        # Emulate a connection close by the database.
+        connection._close()
+        # Even then is_usable() should not raise an exception.
+        try:
+            self.assertFalse(connection.is_usable())
+        finally:
+            # Clean up the mess created by connection._close(). Since the
+            # connection is already closed, this crashes on some backends.
+            try:
+                connection.close()
+            except Exception:
+                pass
+
+
 # We don't make these tests conditional because that means we would need to
 # check and differentiate between:
 # * MySQL+InnoDB, MySQL+MYISAM (something we currently can't do).