diff --git a/packages/flutter/lib/src/material/scaffold.dart b/packages/flutter/lib/src/material/scaffold.dart
index 5be81b2..7757cf1 100644
--- a/packages/flutter/lib/src/material/scaffold.dart
+++ b/packages/flutter/lib/src/material/scaffold.dart
@@ -1958,6 +1958,8 @@
   final GlobalKey<DrawerControllerState> _drawerKey = GlobalKey<DrawerControllerState>();
   final GlobalKey<DrawerControllerState> _endDrawerKey = GlobalKey<DrawerControllerState>();
 
+  final GlobalKey _bodyKey = GlobalKey();
+
   /// Whether this scaffold has a non-null [Scaffold.appBar].
   bool get hasAppBar => widget.appBar != null;
   /// Whether this scaffold has a non-null [Scaffold.drawer].
@@ -2653,7 +2655,7 @@
       widget.body == null ? null : _BodyBuilder(
         extendBody: widget.extendBody,
         extendBodyBehindAppBar: widget.extendBodyBehindAppBar,
-        body: widget.body!,
+        body: KeyedSubtree(key: _bodyKey, child: widget.body!),
       ),
       _ScaffoldSlot.body,
       removeLeftPadding: false,
diff --git a/packages/flutter/test/material/scaffold_test.dart b/packages/flutter/test/material/scaffold_test.dart
index b970288..d39ce30 100644
--- a/packages/flutter/test/material/scaffold_test.dart
+++ b/packages/flutter/test/material/scaffold_test.dart
@@ -12,6 +12,39 @@
 import '../widgets/semantics_tester.dart';
 
 void main() {
+  // Regression test for https://github.com/flutter/flutter/issues/103741
+  testWidgets('extendBodyBehindAppBar change should not cause the body widget lose state', (WidgetTester tester) async {
+    final ScrollController controller = ScrollController();
+    Widget buildFrame({required bool extendBodyBehindAppBar}) {
+      return MediaQuery(
+        data: const MediaQueryData(),
+        child: Directionality(
+          textDirection: TextDirection.ltr,
+          child: Scaffold(
+            extendBodyBehindAppBar: extendBodyBehindAppBar,
+            resizeToAvoidBottomInset: false,
+            body: SingleChildScrollView(
+              controller: controller,
+              child: const FlutterLogo(
+                size: 1107,
+              ),
+            ),
+          ),
+        ),
+      );
+    }
+
+    await tester.pumpWidget(buildFrame(extendBodyBehindAppBar: true));
+    expect(controller.position.pixels, 0.0);
+
+    controller.jumpTo(100.0);
+    await tester.pump();
+    expect(controller.position.pixels, 100.0);
+
+    await tester.pumpWidget(buildFrame(extendBodyBehindAppBar: false));
+    expect(controller.position.pixels, 100.0);
+  });
+
   testWidgets('Scaffold drawer callback test', (WidgetTester tester) async {
     bool isDrawerOpen = false;
     bool isEndDrawerOpen = false;
@@ -2402,6 +2435,7 @@
       '   ancestor was:\n'
       '     Builder\n'
       '   The ancestors of this widget were:\n'
+      '     KeyedSubtree-[GlobalKey#00000]\n'
       '     _BodyBuilder\n'
       '     MediaQuery\n'
       '     LayoutId-[<_ScaffoldSlot.body>]\n'