diff --git a/.github/workflows/health-check.yml b/.github/workflows/health-check.yml
index 4c0717d..2db7f05 100644
--- a/.github/workflows/health-check.yml
+++ b/.github/workflows/health-check.yml
@@ -17,6 +17,7 @@ jobs:
   linkinator:
     name: Crawl live sites for broken links
     runs-on: ubuntu-latest
+    timeout-minutes: 45
     steps:
       - name: Setup Node
         uses: actions/setup-node@v4
diff --git a/404.html b/404.html
index a9244c3..394ae83 100644
--- a/404.html
+++ b/404.html
@@ -2,6 +2,7 @@
 <html lang="en">
 <head>
 <meta charset="UTF-8">
+<base href="/">
     <meta http-equiv="Content-Security-Policy" content="default-src 'self'; script-src 'self' 'unsafe-inline'; style-src 'self' 'unsafe-inline'; img-src 'self' data: https:; font-src 'self' data:; connect-src 'self' https://api.github.com; frame-ancestors 'none'; base-uri 'self'; form-action 'self'">
     <meta http-equiv="X-Content-Type-Options" content="nosniff">
     <meta name="referrer" content="strict-origin-when-cross-origin">
diff --git a/tests/not-found.spec.js b/tests/not-found.spec.js
new file mode 100644
index 0000000..ba61f9d
--- /dev/null
+++ b/tests/not-found.spec.js
@@ -0,0 +1,33 @@
+// @ts-check
+const { test, expect } = require('@playwright/test');
+
+const BASE = process.env.BASE_URL || 'http://localhost:8080';
+const MISSING = '/no/such/page/';
+
+// GitHub Pages serves /404.html at whatever path was requested, so the page's
+// stylesheet, scripts and links must resolve from the site root. Relative
+// URLs resolved under the missing path instead: every asset 404'd, and a link
+// checker following them generated ever-deeper missing paths without end.
+test.describe('404 page served at a nested missing path', () => {
+  test('its assets load and its links resolve from the site root', async ({ page }) => {
+    const failed = [];
+    page.on('response', (r) => {
+      const url = r.url();
+      if (url.startsWith(BASE) && r.status() >= 400 && new URL(url).pathname !== MISSING) {
+        failed.push(`${r.status()} ${url}`);
+      }
+    });
+    const res = await page.goto(`${BASE}${MISSING}`);
+    expect(res && res.status()).toBe(404);
+    await page.waitForLoadState('networkidle');
+    expect(failed).toEqual([]);
+
+    const internal = await page.$$eval('a[href]', (as) =>
+      as.map((a) => a.href).filter((h) => h.startsWith(location.origin)),
+    );
+    expect(internal.length).toBeGreaterThan(0);
+    for (const href of internal) {
+      expect(new URL(href).pathname.startsWith(MISSING), href).toBe(false);
+    }
+  });
+});