diff --git a/ci/conda_env_cpp.txt b/ci/conda_env_cpp.txt
index 4ca76a7215869..902c952532b62 100644
--- a/ci/conda_env_cpp.txt
+++ b/ci/conda_env_cpp.txt
@@ -27,7 +27,7 @@ gflags
 glog
 gmock>=1.10.0
 google-cloud-cpp>=1.34.0
-grpc-cpp
+grpc-cpp<=1.50.1
 gtest>=1.10.0
 libprotobuf
 libutf8proc
diff --git a/cpp/src/arrow/flight/flight_test.cc b/cpp/src/arrow/flight/flight_test.cc
index 502a7898401fa..5520dfc48f746 100644
--- a/cpp/src/arrow/flight/flight_test.cc
+++ b/cpp/src/arrow/flight/flight_test.cc
@@ -1023,7 +1023,7 @@ TEST_F(TestFlightClient, TimeoutFires) {
   Status status = client->GetFlightInfo(options, FlightDescriptor{}).status();
   auto end = std::chrono::system_clock::now();
 #ifdef ARROW_WITH_TIMING_TESTS
-  EXPECT_LE(end - start, std::chrono::milliseconds{400});
+  EXPECT_LE(end - start, std::chrono::milliseconds{1200});
 #else
   ARROW_UNUSED(end - start);
 #endif
diff --git a/cpp/src/arrow/flight/test_definitions.cc b/cpp/src/arrow/flight/test_definitions.cc
index 9d08c70df1542..507c5ef40421c 100644
--- a/cpp/src/arrow/flight/test_definitions.cc
+++ b/cpp/src/arrow/flight/test_definitions.cc
@@ -108,7 +108,11 @@ void ConnectivityTest::TestBrokenConnection() {
   ASSERT_OK(server->Shutdown());
   ASSERT_OK(server->Wait());
 
-  ASSERT_RAISES(IOError, client->GetFlightInfo(FlightDescriptor::Command("")));
+  auto status = client->GetFlightInfo(FlightDescriptor::Command(""));
+  ASSERT_NOT_OK(status);
+  ASSERT_THAT(
+      status.status().code(),
+      ::testing::AnyOf(::arrow::StatusCode::IOError, ::arrow::StatusCode::UnknownError));
 }
 
 //------------------------------------------------------------