diff --git a/server/src/__tests__/heartbeat-issue-liveness-escalation.test.ts b/server/src/__tests__/heartbeat-issue-liveness-escalation.test.ts
index 13f770a6b1..c286393294 100644
--- a/server/src/__tests__/heartbeat-issue-liveness-escalation.test.ts
+++ b/server/src/__tests__/heartbeat-issue-liveness-escalation.test.ts
@@ -698,6 +698,36 @@ describeEmbeddedPostgres("heartbeat resolved dependency wake reconciliation", ()
     expect(wakes.some((wake) => ["queued", "claimed", "completed"].includes(wake.status))).toBe(true);
   });
 
+  it.each(["paused", "terminated", "pending_approval"] as const)(
+    "skips resolved-dependency backstop candidates whose assignee is %s",
+    async (assigneeStatus) => {
+      await enableAutoRecovery();
+      const { companyId, agentId, blockedIssueId } =
+        await seedResolvedDependencyBackstopFixture({ workspaceState: "none" });
+      // Flip the assignee into a directly non-invokable state. The backstop
+      // must drop the candidate at the SQL layer — otherwise it enqueues a
+      // wake that always fails with 409 and loops on every heartbeat.
+      await db.update(agents).set({ status: assigneeStatus }).where(eq(agents.id, agentId));
+
+      const result = await heartbeatService(db).reconcileIssueGraphLiveness();
+
+      expect(result.dependencyWakeBackstopChecked).toBe(0);
+      expect(result.dependencyWakesHealed).toBe(0);
+      expect(result.dependencyWakeIssueIds).not.toContain(blockedIssueId);
+
+      const wakes = await db
+        .select({ id: agentWakeupRequests.id })
+        .from(agentWakeupRequests)
+        .where(
+          and(
+            eq(agentWakeupRequests.companyId, companyId),
+            eq(agentWakeupRequests.reason, "issue_blockers_resolved"),
+          ),
+        );
+      expect(wakes).toHaveLength(0);
+    },
+  );
+
   it("waits for workspace finalize before healing a resolved blocked dependent", async () => {
     const { companyId, agentId, blockedIssueId, blockerIssueId, executionWorkspaceId } =
       await seedResolvedDependencyBackstopFixture({ workspaceState: "not_finalized" });
diff --git a/server/src/services/recovery/service.ts b/server/src/services/recovery/service.ts
index 648a96761c..6cf6a2bdb6 100644
--- a/server/src/services/recovery/service.ts
+++ b/server/src/services/recovery/service.ts
@@ -102,7 +102,7 @@ import {
   buildIssueBlockersResolvedWakeStateKey,
   findExistingIssueBlockersResolvedWakeForReadyState,
 } from "../issue-dependency-wakeups.js";
-import { evaluateAgentInvokabilityFromDb } from "../agent-invokability.js";
+import { DIRECT_NON_INVOKABLE_STATUSES, evaluateAgentInvokabilityFromDb } from "../agent-invokability.js";
 import { isHeartbeatWakeOnDemandEnabled } from "../heartbeat-policy.js";
 import {
   DEFAULT_MAX_SUCCESSFUL_RUN_HANDOFF_ATTEMPTS,
@@ -5219,6 +5219,16 @@ export function recoveryService(
         isNull(issues.conversationAgentId),
         visibleIssueCondition(),
         sql`${issues.assigneeAgentId} is not null`,
+        // Skip candidates whose assignee is directly non-invokable (paused,
+        // terminated, pending_approval). Without this filter the backstop
+        // repeatedly enqueues wakes that always fail with 409, producing a
+        // steady stream of `wake_target_not_invokable` warnings for the same
+        // issue every heartbeat until an operator intervenes. Matches the
+        // atomic guard in the heartbeat's `agents.status -> running` update.
+        // Org-chain invalidity is not covered here for cost reasons; the
+        // enqueue path still filters those cases via
+        // `evaluateAgentInvokabilityFromDb`.
+        notInArray(agents.status, [...DIRECT_NON_INVOKABLE_STATUSES]),
       ];
       if (opts?.companyId) filters.push(eq(issues.companyId, opts.companyId));
       if (afterIssueId) filters.push(gt(issues.id, afterIssueId));
@@ -5241,6 +5251,7 @@ export function recoveryService(
           })
           .from(issueRelations)
           .innerJoin(issues, eq(issueRelations.relatedIssueId, issues.id))
+          .innerJoin(agents, eq(agents.id, issues.assigneeAgentId))
           .where(and(...filters))
           .orderBy(asc(issues.id))
           .limit(RESOLVED_DEPENDENCY_WAKE_BACKSTOP_CANDIDATE_LIMIT);
@@ -5256,6 +5267,7 @@ export function recoveryService(
           totalCount: sql<number>`count(*) over()::int`,
         })
         .from(issues)
+        .innerJoin(agents, eq(agents.id, issues.assigneeAgentId))
         .where(and(...filters))
         .orderBy(asc(issues.id))
         .limit(RESOLVED_DEPENDENCY_WAKE_BACKSTOP_CANDIDATE_LIMIT);