diff --git a/app/Actions/UpdateMentionedOrganizations.php b/app/Actions/UpdateMentionedOrganizations.php
index 31546db70..957533808 100644
--- a/app/Actions/UpdateMentionedOrganizations.php
+++ b/app/Actions/UpdateMentionedOrganizations.php
@@ -9,6 +9,7 @@
 use App\Models\Profile;
 use Carbon\CarbonImmutable;
 use Closure;
+use Illuminate\Http\Client\RequestException;
 use Illuminate\Support\Facades\Cache;
 use Illuminate\Support\Facades\DB;
 use Illuminate\Support\Str;
@@ -39,8 +40,9 @@ public function __construct(
     /**
      * Asks GitHub about the lowercase handles that are neither a user's nor a known organization's, and refreshes the
      * known organizations among them once their profile is a day old. A handle that isn't an organization's isn't asked
-     * about again for a day, and an organization GitHub no longer has is deleted, with the links to it. Returns when to
-     * try again if the rate limit cut the lookups short.
+     * about again for a day, and an organization GitHub no longer has is deleted, with the links to it. An
+     * organization that keeps GitHub from showing it to the app, with an IP allow list for one, is skipped. Returns when
+     * to try again if the rate limit cut the lookups short.
      *
      * @param  list<string>  $handles
      */
@@ -89,7 +91,20 @@ function () use ($organization): void {
         }
 
         foreach ($lookups as [$lookUp, $notFound]) {
-            $account = $lookUp();
+            try {
+                $account = $lookUp();
+            } catch (RequestException $exception) {
+                // The refusals an organization sets up, as in HttpGitHubProvider::organizationMembership(): an IP
+                // allow list, SAML single sign-on or OAuth App access restrictions. Any other one, a rate limit among
+                // them, is retried.
+                $response = $exception->response;
+
+                if (! $response->forbidden() || (! $response->hasHeader('X-GitHub-SSO') && ! Str::contains($response->fluent()->string('message')->value(), ['IP allow list', 'OAuth App access restrictions']))) {
+                    throw $exception;
+                }
+
+                continue;
+            }
 
             if (($account['type'] ?? null) !== 'Organization') {
                 $notFound();
diff --git a/tests/Unit/Actions/UpdateCommitTopicsTest.php b/tests/Unit/Actions/UpdateCommitTopicsTest.php
index 40bb954d3..a0cfbd39c 100644
--- a/tests/Unit/Actions/UpdateCommitTopicsTest.php
+++ b/tests/Unit/Actions/UpdateCommitTopicsTest.php
@@ -230,12 +230,18 @@ function gitHubOrganization(array $account = []): array
     expect(Cache::has('github-organizations:paused'))->toBeFalse();
 });
 
-it('throws when GitHub fails, so the job tries again', function (): void {
+it('throws when GitHub fails, rate limits or forbids anything else, so the job tries again', function (Psr7Response $response): void {
     $github = $this->mock(GitHubProvider::class);
     $github->shouldReceive('rateLimit')->andReturnNull();
-    $github->shouldReceive('accountByLogin')->with('laravel')->andThrow(new RequestException(new Response(new Psr7Response(502))));
+    $github->shouldReceive('accountByLogin')->with('laravel')->andThrow(new RequestException(new Response($response)));
 
     $commit = Commit::factory()->create(['body' => '@laravel', 'mentions' => []]);
 
     expect(fn () => resolve(UpdateCommitTopics::class)->handle($commit))->toThrow(RequestException::class);
-});
+})->with([
+    'an error' => fn (): Psr7Response => new Psr7Response(502),
+    'the primary rate limit' => fn (): Psr7Response => new Psr7Response(403, ['X-RateLimit-Remaining' => '0']),
+    'a secondary rate limit' => fn (): Psr7Response => new Psr7Response(403, ['Retry-After' => '60']),
+    'a secondary rate limit without headers' => fn (): Psr7Response => new Psr7Response(403, [], '{"message":"You have exceeded a secondary rate limit. Please wait a few minutes before you try again."}'),
+    'any other refusal' => fn (): Psr7Response => new Psr7Response(403, [], '{"message":"Resource not accessible by integration"}'),
+]);
diff --git a/tests/Unit/Jobs/LookUpUserOrganizationsTest.php b/tests/Unit/Jobs/LookUpUserOrganizationsTest.php
index 8abf976c0..9a01224dd 100644
--- a/tests/Unit/Jobs/LookUpUserOrganizationsTest.php
+++ b/tests/Unit/Jobs/LookUpUserOrganizationsTest.php
@@ -8,6 +8,9 @@
 use App\Jobs\LookUpUserOrganizations;
 use App\Models\Profile;
 use App\Models\User;
+use GuzzleHttp\Psr7\Response as Psr7Response;
+use Illuminate\Http\Client\RequestException;
+use Illuminate\Http\Client\Response;
 use Illuminate\Support\Facades\Cache;
 use Illuminate\Support\Facades\Queue;
 
@@ -25,6 +28,31 @@
     expect(Profile::query()->where('type', ProfileType::Organization)->pluck('handle')->all())->toBe(['laravel']);
 });
 
+it('skips the organizations that keep GitHub from showing them, and looks the others up', function (Psr7Response $response): void {
+    $forbidden = new RequestException(new Response($response));
+    $github = $this->mock(GitHubProvider::class);
+    $github->shouldReceive('rateLimit')->andReturnNull();
+    $github->shouldReceive('accountByLogin')->with('restricted')->once()->andThrow($forbidden);
+    $github->shouldReceive('accountByLogin')->with('laravel')->once()->andReturn(['login' => 'laravel', 'id' => 958072, 'type' => 'Organization', 'name' => 'Laravel', 'avatar_url' => null, 'bio' => null, 'location' => null, 'blog' => '', 'company' => null]);
+    $github->shouldReceive('account')->with('1')->once()->andThrow($forbidden);
+    $github->shouldReceive('account')->with('6764390')->once()->andReturn(['login' => 'symfony', 'id' => 6764390, 'type' => 'Organization', 'name' => 'Symfony, SAS', 'avatar_url' => null, 'bio' => null, 'location' => null, 'blog' => '', 'company' => null]);
+
+    $private = Profile::factory()->organization()->create(['github_id' => '1', 'handle' => 'private', 'name' => 'Private', 'github_synced_at' => now()->subDays(2)]);
+    $symfony = Profile::factory()->organization()->create(['github_id' => '6764390', 'handle' => 'symfony', 'name' => 'Symfony', 'github_synced_at' => now()->subDays(2)]);
+    $user = User::factory()->create(['bio' => 'Thanks @restricted and @laravel', 'company' => '@private @symfony']);
+
+    dispatch_sync(new LookUpUserOrganizations($user));
+
+    expect(Profile::query()->where('type', ProfileType::Organization)->orderBy('handle')->pluck('handle')->all())->toBe(['laravel', 'private', 'symfony'])
+        ->and($private->refresh()->name)->toBe('Private')
+        ->and($symfony->refresh()->name)->toBe('Symfony, SAS')
+        ->and(Cache::has('github-organizations:not-found:restricted'))->toBeFalse();
+})->with([
+    'an IP allow list' => fn (): Psr7Response => new Psr7Response(403, [], '{"message":"Although you appear to have the correct authorization credentials, the `acme` organization has an IP allow list enabled, and your IP address is not permitted to access this resource."}'),
+    'SAML single sign-on' => fn (): Psr7Response => new Psr7Response(403, ['X-GitHub-SSO' => 'required; url=https://github.com/orgs/acme/sso'], '{"message":"Resource protected by organization SAML enforcement."}'),
+    'OAuth app access restrictions' => fn (): Psr7Response => new Psr7Response(403, [], '{"message":"Although you appear to have the correct authorization credentials, the `acme` organization has enabled OAuth App access restrictions, meaning that data access to third-parties is limited."}'),
+]);
+
 it('runs again once the rate limit resets when it cut the lookups short', function (): void {
     $github = $this->mock(GitHubProvider::class);
     $github->shouldNotReceive('accountByLogin');