diff --git a/src/beaver_gateway/frontends/markdown/frontend.py b/src/beaver_gateway/frontends/markdown/frontend.py
index 5ac934f..58ae12b 100644
--- a/src/beaver_gateway/frontends/markdown/frontend.py
+++ b/src/beaver_gateway/frontends/markdown/frontend.py
@@ -934,22 +934,32 @@ async def _events_with_heartbeat(
     instead of leaving it dangling.
     """
     src = events.__aiter__()
-    while True:
-        next_task: asyncio.Task[Any] = asyncio.ensure_future(src.__anext__())
-        try:
+    next_task: asyncio.Task[Any] | None = None
+    try:
+        while True:
+            # Reuse the in-flight task across timeouts. Spawning a fresh
+            # ``__anext__()`` while the previous one is still pending
+            # puts two consumers on the same async generator — that
+            # raises ``RuntimeError: anext(): asynchronous generator is
+            # already running``.
+            if next_task is None:
+                next_task = asyncio.ensure_future(src.__anext__())
             done, _pending = await asyncio.wait({next_task}, timeout=interval)
-        except BaseException:
+            if not done:
+                yield None
+                continue
+            task = next_task
+            next_task = None
+            try:
+                result = task.result()
+            except StopAsyncIteration:
+                return
+            yield result
+    finally:
+        if next_task is not None and not next_task.done():
             next_task.cancel()
             with contextlib.suppress(BaseException):
                 await next_task
-            raise
-        if not done:
-            yield None
-            continue
-        try:
-            yield next_task.result()
-        except StopAsyncIteration:
-            return
 
 
 def _sse_pack(event: str, data: dict[str, Any]) -> bytes: