diff --git a/wagtail/search/backends/base.py b/wagtail/search/backends/base.py
index 9e73f1199b..ae27ab7fd8 100644
--- a/wagtail/search/backends/base.py
+++ b/wagtail/search/backends/base.py
@@ -299,6 +299,7 @@ class BaseSearchBackend:
     autocomplete_query_compiler_class = None
     results_class = None
     rebuilder_class = None
+    catch_indexing_errors = False
 
     def __init__(self, params):
         pass
diff --git a/wagtail/search/backends/elasticsearch2.py b/wagtail/search/backends/elasticsearch2.py
index da42a7f3e5..57381ec392 100644
--- a/wagtail/search/backends/elasticsearch2.py
+++ b/wagtail/search/backends/elasticsearch2.py
@@ -1006,6 +1006,7 @@ class Elasticsearch2SearchBackend(BaseSearchBackend):
     mapping_class = Elasticsearch2Mapping
     basic_rebuilder_class = ElasticsearchIndexRebuilder
     atomic_rebuilder_class = ElasticsearchAtomicIndexRebuilder
+    catch_indexing_errors = True
 
     settings = {
         'settings': {
diff --git a/wagtail/search/index.py b/wagtail/search/index.py
index a0e70fac28..bb779f73c2 100644
--- a/wagtail/search/index.py
+++ b/wagtail/search/index.py
@@ -154,9 +154,19 @@ def insert_or_update_object(instance):
             try:
                 backend.add(indexed_instance)
             except Exception:
-                # Catch and log all errors
+                # Log all errors
                 logger.exception("Exception raised while adding %r into the '%s' search backend", indexed_instance, backend_name)
 
+                # Catch exceptions for backends that use an external service like Elasticsearch
+                # This is to prevent data loss if that external service was to go down and the user's
+                # save request was to fail.
+                # But note that we don't want this for database backends though as an error during a
+                # database transaction will require the transaction to be rolled back anyway. So If
+                # we caught the error here, the request will only crash again when the next database
+                # query is made but then the error message wouldn't be very informative.
+                if not backend.catch_indexing_errors:
+                    raise
+
 
 def remove_object(instance):
     indexed_instance = get_indexed_instance(instance, check_exists=False)
@@ -166,9 +176,14 @@ def remove_object(instance):
             try:
                 backend.delete(indexed_instance)
             except Exception:
-                # Catch and log all errors
+                # Log all errors
                 logger.exception("Exception raised while deleting %r from the '%s' search backend", indexed_instance, backend_name)
 
+                # Only catch the exception if the backend requires this
+                # See the comments in insert_or_update_object for an explanation
+                if not backend.catch_indexing_errors:
+                    raise
+
 
 class BaseField:
     def __init__(self, field_name, **kwargs):