diff --git a/tests/federation_connectivity_test.go b/tests/federation_connectivity_test.go
new file mode 100644
index 0000000..ef6e0ec
--- /dev/null
+++ b/tests/federation_connectivity_test.go
@@ -0,0 +1,106 @@
+package tests
+
+import (
+	"testing"
+	"time"
+
+	"github.com/matrix-org/complement-crypto/internal/api"
+	"github.com/matrix-org/complement/helpers"
+)
+
+// A and B are in a room, on different servers.
+// B's server goes offline.
+// C joins the room (on A's server).
+// C sends a message. C will not be able to get device keys for B.
+// B comes back online.
+// B will be unable to decrypt C's message. TODO: how to fix?
+// Ensure sending another message from C is decryptable.
+func TestNewUserCannotGetKeysForOfflineServer(t *testing.T) {
+	deployment := Deploy(t)
+	csapiAlice := deployment.Register(t, "hs1", helpers.RegistrationOpts{
+		LocalpartSuffix: "alice",
+		Password:        "complement-crypto-password",
+	})
+	csapiBob := deployment.Register(t, "hs2", helpers.RegistrationOpts{
+		LocalpartSuffix: "bob",
+		Password:        "complement-crypto-password",
+	})
+	csapiCharlie := deployment.Register(t, "hs1", helpers.RegistrationOpts{
+		LocalpartSuffix: "charlie",
+		Password:        "complement-crypto-password",
+	})
+	roomID := csapiAlice.MustCreateRoom(t, map[string]interface{}{
+		"preset": "private_chat",
+		"invite": []string{csapiBob.UserID},
+		"initial_state": []map[string]interface{}{
+			{
+				"type":      "m.room.encryption",
+				"state_key": "",
+				"content": map[string]interface{}{
+					"algorithm": "m.megolm.v1.aes-sha2",
+				},
+			},
+		},
+	})
+
+	csapiBob.MustJoinRoom(t, roomID, []string{"hs1"})
+
+	ss := deployment.SlidingSyncURL(t)
+	alice := MustLoginClient(t, api.ClientType{HS: "hs1", Lang: api.ClientTypeRust}, api.FromComplementClient(csapiAlice, "complement-crypto-password"), ss)
+	defer alice.Close(t)
+	bob := MustLoginClient(t, api.ClientType{HS: "hs2", Lang: api.ClientTypeJS}, api.FromComplementClient(csapiBob, "complement-crypto-password"), ss)
+	defer bob.Close(t)
+	aliceStopSyncing := alice.StartSyncing(t)
+	defer aliceStopSyncing()
+	bobStopSyncing := bob.StartSyncing(t)
+	defer bobStopSyncing()
+
+	// let clients sync device keys
+	time.Sleep(time.Second)
+
+	// ensure encrypted messaging works
+	wantMsgBody := "Hello world"
+	waiter := bob.WaitUntilEventInRoom(t, roomID, api.CheckEventHasBody(wantMsgBody))
+	evID := alice.SendMessage(t, roomID, wantMsgBody)
+	t.Logf("bob (%s) waiting for event %s", bob.Type(), evID)
+	waiter.Wait(t, 5*time.Second)
+
+	// now bob's HS becomes unreachable
+	deployment.PauseServer(t, "hs2")
+
+	// C now joins the room
+	csapiAlice.MustInviteRoom(t, roomID, csapiCharlie.UserID)
+	charlie := MustLoginClient(t, api.ClientType{HS: "hs1", Lang: api.ClientTypeRust}, api.FromComplementClient(csapiCharlie, "complement-crypto-password"), ss)
+	defer charlie.Close(t)
+	charlieStopSyncing := charlie.StartSyncing(t)
+	defer charlieStopSyncing()
+	csapiCharlie.MustJoinRoom(t, roomID, []string{"hs1"})
+
+	// let charlie sync device keys... and fail to get bob's keys!
+	time.Sleep(time.Second)
+
+	// send a message: bob won't be able to decrypt this, but alice will.
+	wantMsgBody = "Bob can't see this because his server is down"
+	waiter = alice.WaitUntilEventInRoom(t, roomID, api.CheckEventHasBody(wantMsgBody))
+	evID = charlie.SendMessage(t, roomID, wantMsgBody)
+	t.Logf("alice (%s) waiting for event %s", alice.Type(), evID)
+	waiter.Wait(t, 5*time.Second)
+
+	// now bob's server comes back online
+	deployment.UnpauseServer(t, "hs2")
+
+	// now we need to wait a bit for charlie's client to decide to hit /keys/claim again.
+	// If the client hits too often, there will be constantly send lag so long as bob's HS is offline.
+	// If the client hits too infrequently, there will be multiple undecryptable messages.
+	// See https://github.com/matrix-org/matrix-rust-sdk/issues/281 for why we want to backoff.
+	// See https://github.com/matrix-org/matrix-rust-sdk/issues/2804 for discussions on what the backoff should be.
+	t.Logf("sleeping until client timeout is ready...")
+	time.Sleep(20 * time.Second)
+
+	// send another message, bob should be able to decrypt it.
+	wantMsgBody = "Bob can see this because his server is now back online"
+	waiter = bob.WaitUntilEventInRoom(t, roomID, api.CheckEventHasBody(wantMsgBody))
+	evID = charlie.SendMessage(t, roomID, wantMsgBody)
+	t.Logf("bob (%s) waiting for event %s", bob.Type(), evID)
+	waiter.Wait(t, 5*time.Second)
+}