diff --git a/src/store/chatStore.ts b/src/store/chatStore.ts
index 6b8a112c8..131854fd2 100644
--- a/src/store/chatStore.ts
+++ b/src/store/chatStore.ts
@@ -1762,6 +1762,15 @@ const chatStore = (initial?: Partial<ChatStore>) =>
 
       // Create AbortController for this task's SSE connection
       // First check if there's already an active SSE connection for this task
+      if (activeSSEControllers[newTaskId] && type === 'replay') {
+        // A history replay must never tear down a live run's stream: the
+        // ongoing run is the fresher state, and aborting it kills the run
+        // on the backend. Leave the live connection alone.
+        console.warn(
+          `Task ${newTaskId} already has an active SSE connection, skipping history replay`
+        );
+        return;
+      }
       if (activeSSEControllers[newTaskId]) {
         console.warn(
           `Task ${newTaskId} already has an active SSE connection, aborting old one`
diff --git a/src/store/projectStore.ts b/src/store/projectStore.ts
index 402ada3de..beae3913c 100644
--- a/src/store/projectStore.ts
+++ b/src/store/projectStore.ts
@@ -31,7 +31,11 @@ import {
 } from '@/types/constants';
 import { create } from 'zustand';
 import { getAuthStore } from './authStore';
-import { createChatStoreInstance, VanillaChatStore } from './chatStore';
+import {
+  createChatStoreInstance,
+  hasActiveSSEConnection,
+  VanillaChatStore,
+} from './chatStore';
 import {
   projectMetaFromServer,
   useSpaceStore,
@@ -1042,6 +1046,18 @@ const projectStore = create<ProjectStore>()((set, get) => ({
     ) {
       return;
     }
+    // Never evict a project that still has a live run. Eviction drops the
+    // runtime chat stores, so returning to the project rebuilds it from
+    // history and replays the ongoing task id -- which aborts the live
+    // run's stream and kills the run on the backend. Keep the stale flag
+    // so the eviction simply happens on a later, safe transition.
+    const outgoingProject = get().projects[previousProjectId];
+    const outgoingTaskIds = Object.values(
+      outgoingProject?.chatStores ?? {}
+    ).flatMap((chatStore) => Object.keys(chatStore.getState().tasks));
+    if (hasActiveSSEConnection(outgoingTaskIds)) {
+      return;
+    }
     // _evictProjectRuntime handles staleProjectIds cleanup itself.
     get()._evictProjectRuntime(previousProjectId);
   },