diff --git a/static/sessions.js b/static/sessions.js
index ab416550..5dda0ba9 100644
--- a/static/sessions.js
+++ b/static/sessions.js
@@ -3694,9 +3694,16 @@ function _installSidebarSseFocusHook(){
   });
   window.addEventListener('focus', () => {
     if(_sidebarSseBlurCloseTimer){ clearTimeout(_sidebarSseBlurCloseTimer); _sidebarSseBlurCloseTimer = 0; }
-    // Reopen (both ensure-idempotent) and catch up on anything missed while blurred.
+    // Reopen and catch up on anything missed while blurred. ensureSessionEventsSSE()
+    // is idempotent (`if(_sessionEventsSSE) return`), but startGatewaySSE() is NOT — it
+    // begins with an unconditional stopGatewaySSE(). So only reopen the gateway when it
+    // was actually closed; otherwise a transient blur shorter than the debounce (where
+    // the blur-close timer was cleared and the stream was never torn down) would
+    // drop+reconnect the live gateway on every window switch, cancelling its poll
+    // fallback and resetting probe/warning state — the exact thrash the debounce exists
+    // to prevent, in the multi-window scenario this fix targets (#4151).
     ensureSessionEventsSSE();
-    startGatewaySSE();
+    if(!_gatewaySSE) startGatewaySSE();
     void refreshSessionList('focus');
   });
 }
diff --git a/tests/test_issue4151_pwa_focus_sse.py b/tests/test_issue4151_pwa_focus_sse.py
index eb385cbb..bcf60d45 100644
--- a/tests/test_issue4151_pwa_focus_sse.py
+++ b/tests/test_issue4151_pwa_focus_sse.py
@@ -50,7 +50,7 @@ def test_focus_hook_closes_both_global_sidebar_streams():
     """The blur path closes the session-events AND gateway streams."""
     assert "function _installSidebarSseFocusHook()" in SESSIONS_JS
     start = SESSIONS_JS.find("function _installSidebarSseFocusHook()")
-    block = SESSIONS_JS[start:start + 1100]
+    block = SESSIONS_JS[start:start + 1700]
     # Installed once.
     assert "_hermesSidebarSseFocusHook" in block
     # Blur listener tears down both global streams.
@@ -70,7 +70,7 @@ def test_blur_close_is_debounced_and_rechecks_focus_at_fire_time():
     when it fires, so focus returning during the debounce cancels the teardown.
     """
     start = SESSIONS_JS.find("function _installSidebarSseFocusHook()")
-    block = SESSIONS_JS[start:start + 1100]
+    block = SESSIONS_JS[start:start + 1700]
     assert "_sidebarSseBlurCloseTimer" in block
     assert "setTimeout(" in block
     # Re-check guards the actual close so a returned focus is a no-op.
@@ -79,6 +79,34 @@ def test_blur_close_is_debounced_and_rechecks_focus_at_fire_time():
     assert "clearTimeout(_sidebarSseBlurCloseTimer)" in block
 
 
+def test_focus_reopen_does_not_thrash_the_gateway_stream():
+    """The focus handler must NOT unconditionally restart the gateway stream.
+
+    startGatewaySSE() begins with an unconditional stopGatewaySSE() (it is NOT
+    idempotent, unlike ensureSessionEventsSSE()'s `if(_sessionEventsSSE) return`).
+    On a transient blur shorter than the 1s debounce, the blur-close timer is
+    cleared and the gateway stream is never torn down — so an unconditional
+    startGatewaySSE() on the following focus would drop+reconnect the live gateway,
+    cancel its poll fallback, and reset probe/warning state on every window switch
+    (the exact thrash the debounce exists to prevent, in the multi-window scenario
+    #4151 targets). The reopen must therefore be guarded on the gateway actually
+    being closed. (greptile P1.)
+    """
+    start = SESSIONS_JS.find("function _installSidebarSseFocusHook()")
+    block = SESSIONS_JS[start:start + 1700]
+    focus_idx = block.find("window.addEventListener('focus'")
+    assert focus_idx != -1
+    focus_body = block[focus_idx:]
+    # The gateway reopen is guarded on the stream being closed (mirrors the
+    # session-events idempotency), not called unconditionally.
+    assert "if(!_gatewaySSE) startGatewaySSE()" in focus_body, (
+        "focus handler must guard startGatewaySSE() on `!_gatewaySSE` so a "
+        "transient blur+focus does not drop+reconnect a still-open gateway stream"
+    )
+    # And it must NOT call startGatewaySSE() bare (unguarded) on focus.
+    assert "\n    startGatewaySSE();" not in focus_body
+
+
 def test_session_events_open_guard_uses_backgrounded_predicate():
     """ensureSessionEventsSSE installs the focus hook and gates open on the predicate."""
     start = SESSIONS_JS.find("function ensureSessionEventsSSE()")
@@ -121,7 +149,7 @@ def test_per_session_stream_NOT_closed_on_blur():
         )
     # (b) the sidebar focus hook only manages the two global streams.
     start = SESSIONS_JS.find("function _installSidebarSseFocusHook()")
-    block = SESSIONS_JS[start:start + 1100]
+    block = SESSIONS_JS[start:start + 1700]
     assert "stopSessionStream" not in block
     assert "startSessionStream" not in block