diff --git a/news/9180.bugfix.rst b/news/9180.bugfix.rst
new file mode 100644
index 00000000000..e597c1ad90a
--- /dev/null
+++ b/news/9180.bugfix.rst
@@ -0,0 +1 @@
+Fix error when an existing incompatibility is unable to be applied to a backtracked state.
diff --git a/news/resolvelib.vendor.rst b/news/resolvelib.vendor.rst
new file mode 100644
index 00000000000..680da3be1e7
--- /dev/null
+++ b/news/resolvelib.vendor.rst
@@ -0,0 +1 @@
+Upgrade resolvelib to 0.5.4.
diff --git a/src/pip/_vendor/resolvelib/__init__.py b/src/pip/_vendor/resolvelib/__init__.py
index 5a400f23ed1..f023ad63154 100644
--- a/src/pip/_vendor/resolvelib/__init__.py
+++ b/src/pip/_vendor/resolvelib/__init__.py
@@ -11,7 +11,7 @@
     "ResolutionTooDeep",
 ]
 
-__version__ = "0.5.3"
+__version__ = "0.5.4"
 
 
 from .providers import AbstractProvider, AbstractResolver
diff --git a/src/pip/_vendor/resolvelib/resolvers.py b/src/pip/_vendor/resolvelib/resolvers.py
index acf0f8a6b43..bb88d8c2c75 100644
--- a/src/pip/_vendor/resolvelib/resolvers.py
+++ b/src/pip/_vendor/resolvelib/resolvers.py
@@ -257,7 +257,7 @@ def _backtrack(self):
             information from Y to Y'.
         4a. If this causes Y' to conflict, we need to backtrack again. Make Y'
             the new Z and go back to step 2.
-        4b. If the incompatibilites apply cleanly, end backtracking.
+        4b. If the incompatibilities apply cleanly, end backtracking.
         """
         while len(self._states) >= 3:
             # Remove the state that triggered backtracking.
@@ -271,28 +271,36 @@ def _backtrack(self):
                 for k, v in broken_state.criteria.items()
             ]
 
+            # Also mark the newly known incompatibility.
+            incompatibilities_from_broken.append((name, [candidate]))
+
             self._r.backtracking(candidate)
 
             # Create a new state from the last known-to-work one, and apply
             # the previously gathered incompatibility information.
-            self._push_new_state()
-            for k, incompatibilities in incompatibilities_from_broken:
-                try:
-                    crit = self.state.criteria[k]
-                except KeyError:
-                    continue
-                self.state.criteria[k] = crit.excluded_of(incompatibilities)
+            def _patch_criteria():
+                for k, incompatibilities in incompatibilities_from_broken:
+                    if not incompatibilities:
+                        continue
+                    try:
+                        criterion = self.state.criteria[k]
+                    except KeyError:
+                        continue
+                    criterion = criterion.excluded_of(incompatibilities)
+                    if criterion is None:
+                        return False
+                    self.state.criteria[k] = criterion
+                return True
 
-            # Mark the newly known incompatibility.
-            criterion = self.state.criteria[name].excluded_of([candidate])
+            self._push_new_state()
+            success = _patch_criteria()
 
             # It works! Let's work on this new state.
-            if criterion:
-                self.state.criteria[name] = criterion
+            if success:
                 return True
 
-            # State does not work after adding the new incompatibility
-            # information. Try the still previous state.
+            # State does not work after applying known incompatibilities.
+            # Try the still previous state.
 
         # No way to backtrack anymore.
         return False
diff --git a/src/pip/_vendor/vendor.txt b/src/pip/_vendor/vendor.txt
index 4f7042cc127..1db32f396ae 100644
--- a/src/pip/_vendor/vendor.txt
+++ b/src/pip/_vendor/vendor.txt
@@ -15,7 +15,7 @@ requests==2.25.0
     chardet==3.0.4
     idna==2.10
     urllib3==1.26.2
-resolvelib==0.5.3
+resolvelib==0.5.4
 retrying==1.3.3
 setuptools==44.0.0
 six==1.15.0