diff --git a/pkg/kv/kvserver/closedts/sidetransport/BUILD.bazel b/pkg/kv/kvserver/closedts/sidetransport/BUILD.bazel
index 8788cff8d3fe..4a88290c13e4 100644
--- a/pkg/kv/kvserver/closedts/sidetransport/BUILD.bazel
+++ b/pkg/kv/kvserver/closedts/sidetransport/BUILD.bazel
@@ -44,6 +44,7 @@ go_test(
         "//pkg/roachpb:with-mocks",
         "//pkg/rpc",
         "//pkg/settings/cluster",
+        "//pkg/testutils",
         "//pkg/util/hlc",
         "//pkg/util/leaktest",
         "//pkg/util/log",
diff --git a/pkg/kv/kvserver/closedts/sidetransport/sender.go b/pkg/kv/kvserver/closedts/sidetransport/sender.go
index 00536eb51a45..3b30c582e995 100644
--- a/pkg/kv/kvserver/closedts/sidetransport/sender.go
+++ b/pkg/kv/kvserver/closedts/sidetransport/sender.go
@@ -107,7 +107,8 @@ type streamState struct {
 }
 
 type connTestingKnobs struct {
-	beforeSend func(destNodeID roachpb.NodeID, msg *ctpb.Update)
+	beforeSend         func(destNodeID roachpb.NodeID, msg *ctpb.Update)
+	sleepOnErrOverride time.Duration
 }
 
 // trackedRange contains the information that the side-transport last published
@@ -666,6 +667,10 @@ type nodeDialer interface {
 	Dial(ctx context.Context, nodeID roachpb.NodeID, class rpc.ConnectionClass) (_ *grpc.ClientConn, err error)
 }
 
+// On sending errors, we sleep a bit as to not spin on a tripped
+// circuit-breaker in the Dialer.
+const sleepOnErr = time.Second
+
 // rpcConn is an implementation of conn that is implemented using a gRPC stream.
 //
 // The connection will read messages from producer.buf. If the buffer overflows
@@ -773,18 +778,23 @@ func (r *rpcConn) run(ctx context.Context, stopper *stop.Stopper) {
 			defer r.cleanupStream(nil /* err */)
 			everyN := log.Every(10 * time.Second)
 
-			// On sending errors, we sleep a bit as to not spin on a tripped
-			// circuit-breaker in the Dialer.
-			const sleepOnErr = time.Second
+			errSleepTime := sleepOnErr
+			if r.testingKnobs.sleepOnErrOverride > 0 {
+				errSleepTime = r.testingKnobs.sleepOnErrOverride
+			}
+
 			for {
 				if ctx.Err() != nil {
 					return
 				}
+				if atomic.LoadInt32(&r.closed) > 0 {
+					return
+				}
 				if err := r.maybeConnect(ctx, stopper); err != nil {
 					if everyN.ShouldLog() {
 						log.Infof(ctx, "side-transport failed to connect to n%d: %s", r.nodeID, err)
 					}
-					time.Sleep(sleepOnErr)
+					time.Sleep(errSleepTime)
 					continue
 				}
 
@@ -797,10 +807,6 @@ func (r *rpcConn) run(ctx context.Context, stopper *stop.Stopper) {
 				if !ok {
 					return
 				}
-				closed := atomic.LoadInt32(&r.closed) > 0
-				if closed {
-					return
-				}
 
 				if msg == nil {
 					// The sequence number we've requested is no longer in the buffer. We
@@ -827,7 +833,7 @@ func (r *rpcConn) run(ctx context.Context, stopper *stop.Stopper) {
 					// should have a blocking version of Dial() that we just leave hanging
 					// and get a notification when it succeeds.
 					r.cleanupStream(err)
-					time.Sleep(sleepOnErr)
+					time.Sleep(errSleepTime)
 				}
 			}
 		})
diff --git a/pkg/kv/kvserver/closedts/sidetransport/sender_test.go b/pkg/kv/kvserver/closedts/sidetransport/sender_test.go
index cceae4ae2fe2..4cf7a2c22abb 100644
--- a/pkg/kv/kvserver/closedts/sidetransport/sender_test.go
+++ b/pkg/kv/kvserver/closedts/sidetransport/sender_test.go
@@ -14,6 +14,7 @@ import (
 	"context"
 	"fmt"
 	"net"
+	"sync/atomic"
 	"testing"
 	"time"
 
@@ -23,6 +24,7 @@ import (
 	"github.com/cockroachdb/cockroach/pkg/roachpb"
 	"github.com/cockroachdb/cockroach/pkg/rpc"
 	"github.com/cockroachdb/cockroach/pkg/settings/cluster"
+	"github.com/cockroachdb/cockroach/pkg/testutils"
 	"github.com/cockroachdb/cockroach/pkg/util/hlc"
 	"github.com/cockroachdb/cockroach/pkg/util/leaktest"
 	"github.com/cockroachdb/cockroach/pkg/util/log"
@@ -547,3 +549,55 @@ func TestSenderReceiverIntegration(t *testing.T) {
 	// Check that the other Receiver is still receiving updates.
 	<-receivers[2].testingKnobs[1].onMsg
 }
+
+type failingDialer struct {
+	dialCount int32
+}
+
+var _ nodeDialer = &failingDialer{}
+
+func (f *failingDialer) Dial(
+	ctx context.Context, nodeID roachpb.NodeID, class rpc.ConnectionClass,
+) (_ *grpc.ClientConn, err error) {
+	atomic.AddInt32(&f.dialCount, 1)
+	return nil, errors.New("failingDialer")
+}
+
+func (f *failingDialer) callCount() int32 {
+	return atomic.LoadInt32(&f.dialCount)
+}
+
+// TestRPCConnStopOnClose verifies that connections that are closed would stop
+// their work loops eagerly even when nodes they are talking to are unreachable.
+func TestRPCConnStopOnClose(t *testing.T) {
+	defer leaktest.AfterTest(t)()
+	defer log.Scope(t).Close(t)
+
+	ctx := context.Background()
+	stopper := stop.NewStopper()
+	defer stopper.Stop(ctx)
+
+	sleepTime := time.Millisecond
+
+	dialer := &failingDialer{}
+	factory := newRPCConnFactory(dialer, connTestingKnobs{sleepOnErrOverride: sleepTime})
+	connection := factory.new(nil, /* sender is not needed as dialer always fails Dial attempts */
+		roachpb.NodeID(1))
+	connection.run(ctx, stopper)
+
+	// Wait for first dial attempt for sanity reasons.
+	testutils.SucceedsSoon(t, func() error {
+		if dialer.callCount() == 0 {
+			return errors.New("connection didn't dial yet")
+		}
+		return nil
+	})
+	connection.close()
+	// Ensure that dialing stops once connection is stopped.
+	testutils.SucceedsSoon(t, func() error {
+		if stopper.NumTasks() > 0 {
+			return errors.New("connection worker didn't stop yet")
+		}
+		return nil
+	})
+}