diff --git a/steam_backlog_enforcer/_shadow.py b/steam_backlog_enforcer/_shadow.py
index 2d762d9..978d17b 100644
--- a/steam_backlog_enforcer/_shadow.py
+++ b/steam_backlog_enforcer/_shadow.py
@@ -128,8 +128,12 @@ def _should_warn(exc: BaseException) -> bool:
     """Whether *exc* was not already logged within :data:`WARN_EVERY_SECONDS`."""
     key = f"{type(exc).__name__}: {exc}"
     now = time.monotonic()
-    last = _last_warned.get(key)
-    if last is not None and now - last < WARN_EVERY_SECONDS:
+    # Forget expired errors first: a message that varies per tick (a JSON
+    # offset, say) must not grow a long-lived daemon's memory without bound.
+    expired = [k for k, at in _last_warned.items() if now - at >= WARN_EVERY_SECONDS]
+    for old in expired:
+        del _last_warned[old]
+    if key in _last_warned:
         return False
     _last_warned[key] = now
     return True
diff --git a/steam_backlog_enforcer/tests/test_shadow_guard.py b/steam_backlog_enforcer/tests/test_shadow_guard.py
index bc3532d..256cb21 100644
--- a/steam_backlog_enforcer/tests/test_shadow_guard.py
+++ b/steam_backlog_enforcer/tests/test_shadow_guard.py
@@ -129,3 +129,17 @@ def test_tick_completes_and_enforced_count_is_untouched(
     assert state.seconds == seconds
     assert state.last_tick_at == T0
     assert state.shadow_per_source == {shadow: 3.0}
+
+
+def test_errors_older_than_the_window_are_forgotten() -> None:
+    """A message that varies per tick must not grow the daemon's memory."""
+    window = _shadow.WARN_EVERY_SECONDS
+    clock = [0.0, 1.0, window + 2.0]
+    errors = [ValueError(f"char {i}") for i in range(3)]
+    with (
+        patch.object(_shadow, "read_now", side_effect=errors),
+        patch.object(_shadow.time, "monotonic", side_effect=clock),
+    ):
+        for _ in errors:
+            observe_shadow({}, stamp=T0)
+    assert list(_shadow._last_warned) == ["ValueError: char 2"]