diff --git a/.github/workflows/ci.yml b/.github/workflows/ci.yml
index 9ce86f2..f5b80a2 100644
--- a/.github/workflows/ci.yml
+++ b/.github/workflows/ci.yml
@@ -16,6 +16,11 @@ jobs:
 
     env:
       PY_VERSION: "3.11"
+      REF_TIMES_model: "b488fb07f0899ee8b7e710c230b1a9414fa06f7d"
+      REF_demos-xlsx: "f956db07a253d4f5c60e108791ab7bb2b8136690"
+      REF_demos-dd: "2848a8a8e2fdcf0cdf7f83eefbdd563b0bb74e86"
+      REF_tim: "e820d8002adc6b1526a3bffcc439219b28d0eed5"
+      REF_tim-gams: "703f6a4e1d0bedd95c3ebdae534496f3a7e1b7cc"
 
     steps:
       - uses: actions/checkout@v3
@@ -48,30 +53,25 @@ jobs:
           source .venv/bin/activate
           pytest
 
-      - name: Cache XLSX cache directory
-        id: cache
-        uses: actions/cache@v4
-        with:
-          path: xl2times/.cache
-          key: ${{ runner.os }}-py-${{ env.PY_VERSION }}
-          save-always: true
-
       # ---------- Prepare ETSAP Demo models
 
       - uses: actions/checkout@v3
         with:
           repository: etsap-TIMES/TIMES_model
           path: TIMES_model
+          ref: ${{ env.REF_TIMES_model }}
 
       - uses: actions/checkout@v3
         with:
           repository: olejandro/demos-dd
           path: xl2times/benchmarks/dd
+          ref: ${{ env.REF_demos-dd }}
 
       - uses: actions/checkout@v3
         with:
           repository: olejandro/demos-xlsx
           path: xl2times/benchmarks/xlsx
+          ref: ${{ env.REF_demos-xlsx }}
           token: ${{ secrets.GH_PAT_DEMOS_XLSX }}
 
       # ---------- Prepare TIMES Ireland Model
@@ -82,11 +82,13 @@ jobs:
         with:
           repository: esma-cgep/tim
           path: xl2times/benchmarks/xlsx/Ireland
+          ref: ${{ env.REF_tim }}
 
       - uses: actions/checkout@v3
         with:
           repository: esma-cgep/tim-gams
           path: xl2times/benchmarks/dd/Ireland
+          ref: ${{ env.REF_tim-gams }}
 
       # ---------- Install GAMS
 
@@ -109,6 +111,18 @@ jobs:
 
       # ---------- Run tool, check for regressions
 
+      - name: Restore XLSX cache directory from cache
+        id: cache
+        uses: actions/cache/restore@v4
+        with:
+          path: xl2times/.cache
+          # Cache key is refs of the input xlsx repos, since that's what is cached
+          key: ${{ runner.os }}-py-${{ env.PY_VERSION }}-${{ env.REF_demos-xlsx }}-${{ env.REF_tim }}
+          # If we can't find the exact key for the TIM repo, still use the cache if the demos repo ref matches
+          restore-keys: |
+            ${{ runner.os }}-py-${{ env.PY_VERSION }}-${{ env.REF_demos-xlsx }}-
+            ${{ runner.os }}-py-${{ env.PY_VERSION }}-
+
       - name: Run tool on all benchmarks
         env:
           GAMS_LICENSE: ${{ secrets.GAMS_LICENSE }}
@@ -147,3 +161,10 @@ jobs:
         run: |
           sed -n '/Benchmark *Time.*Accuracy/h;//!H;$!d;x;//p' out.txt
           exit $(cat retcode.txt)
+
+      - uses: actions/cache/save@v4
+        # Save the cache even if the regression tests fail
+        if: always() && !steps.cache-restore.outputs.cache-hit
+        with:
+          path: xl2times/.cache
+          key: ${{ runner.os }}-py-${{ env.PY_VERSION }}-${{ env.REF_demos-xlsx }}-${{ env.REF_tim }}