diff --git a/Library/Homebrew/dev-cmd/bump.rb b/Library/Homebrew/dev-cmd/bump.rb
index fdbe10bea4..65e5395418 100644
--- a/Library/Homebrew/dev-cmd/bump.rb
+++ b/Library/Homebrew/dev-cmd/bump.rb
@@ -25,6 +25,8 @@ module Homebrew
         timeout:         60,
         retries:         0,
       }.freeze, T::Hash[Symbol, T.untyped])
+      MAX_CONSECUTIVE_GITHUB_API_ERRORS = 5
+      GITHUB_API_ERROR_RETRY_SLEEP = 5
       PYPI_UNSTABLE_VERSION_REGEX = /^(?:\d+!)?\d+(?:\.\d+)*(?:a|b|rc)\d+|\.dev\d+$/i
 
       LIVECHECK_MESSAGE_REGEX = /^(?:error:|skipped|unable to get(?: throttled)? versions)/i
@@ -849,6 +851,7 @@ module Homebrew
                             .flatten
         end
 
+        consecutive_github_api_errors = 0
         formulae_and_casks.each_with_index do |formula_or_cask, i|
           puts if i.positive?
           next if skip_ineligible_formulae!(formula_or_cask)
@@ -863,12 +866,33 @@ module Homebrew
 
           package_data = Repology.single_package_query(name, repository:) unless skip_repology?(formula_or_cask)
 
-          retrieve_and_display_info_and_open_pr(
-            formula_or_cask,
-            name,
-            package_data&.values&.first || [],
-            ambiguous_cask: ambiguous_casks.include?(formula_or_cask),
-          )
+          retried = T.let(false, T::Boolean)
+          begin
+            retrieve_and_display_info_and_open_pr(
+              formula_or_cask,
+              name,
+              package_data&.values&.first || [],
+              ambiguous_cask: ambiguous_casks.include?(formula_or_cask),
+            )
+            consecutive_github_api_errors = 0
+          rescue GitHub::API::RateLimitExceededError, GitHub::API::AuthenticationFailedError
+            # Retrying these for the remaining packages cannot succeed, so stop now.
+            raise
+          rescue GitHub::API::Error => e
+            unless retried
+              retried = true
+              onoe "#{name}: retrying after a GitHub API error: #{e}"
+              sleep GITHUB_API_ERROR_RETRY_SLEEP
+              retry
+            end
+
+            consecutive_github_api_errors += 1
+            if consecutive_github_api_errors >= MAX_CONSECUTIVE_GITHUB_API_ERRORS
+              odie "Aborting after #{consecutive_github_api_errors} consecutive GitHub API errors: #{e}"
+            end
+
+            onoe "#{name}: skipped after a GitHub API error: #{e}"
+          end
         end
       end