diff --git a/src/mkdocstrings_handlers/python/_internal/rendering.py b/src/mkdocstrings_handlers/python/_internal/rendering.py
index d5ffc8e..56a1c39 100644
--- a/src/mkdocstrings_handlers/python/_internal/rendering.py
+++ b/src/mkdocstrings_handlers/python/_internal/rendering.py
@@ -45,6 +45,8 @@
 
 _logger = get_logger(__name__)
 
+_STASH_KEY_ALPHABET = string.ascii_letters + string.digits
+
 
 def _sort_key_alphabetical(item: CollectorItem) -> str:
     # `chr(sys.maxunicode)` is a string that contains the final unicode character,
@@ -107,11 +109,15 @@ class _StashCrossRefFilter:
 
     @staticmethod
     def _gen_key(length: int) -> str:
-        return "_" + "".join(random.choice(string.ascii_letters + string.digits) for _ in range(max(1, length - 1)))  # noqa: S311
+        return "_" + "".join(random.choice(_STASH_KEY_ALPHABET) for _ in range(max(1, length - 1)))  # noqa: S311
 
     def _gen_stash_key(self, length: int) -> str:
         key = self._gen_key(length)
         while key in self.stash:
+            key_length = len(key)
+            keyspace_size = len(_STASH_KEY_ALPHABET) ** (key_length - 1)
+            if sum(len(stash_key) == key_length for stash_key in self.stash) >= keyspace_size:
+                length = key_length + 1
             key = self._gen_key(length)
         return key
 
diff --git a/tests/test_rendering.py b/tests/test_rendering.py
index 91f945a..6ec3ccc 100644
--- a/tests/test_rendering.py
+++ b/tests/test_rendering.py
@@ -54,6 +54,19 @@ def test_format_signature(name: Markup, signature: str) -> None:
         assert rendering._format_signature(name, signature, length)
 
 
+def test_stash_crossref_filter_expands_exhausted_keyspace() -> None:
+    """Assert stashing more cross-references than fit at the requested length terminates."""
+    stash_crossref = rendering._StashCrossRefFilter()
+    stash_crossref.stash.clear()
+    try:
+        keys = [stash_crossref(str(index), length=1) for index in range(63)]
+    finally:
+        stash_crossref.stash.clear()
+
+    assert len(set(keys)) == 63
+    assert len(keys[-1]) == 3
+
+
 @dataclass
 class _FakeObject:
     name: str