diff --git a/src/builder/b-deletion.c b/src/builder/b-deletion.c
index f17bd3d..18dc5a5 100644
--- a/src/builder/b-deletion.c
+++ b/src/builder/b-deletion.c
@@ -584,6 +584,28 @@ saib_jobdir_is_held(const char *vn)
 	return 1;
 }
 
+/*
+ * How many job dirs are held for tasks we are still building... expired holds
+ * are dropped on the way
+ */
+
+unsigned int
+saib_jobdir_holds_live(void)
+{
+	unsigned int n = 0;
+
+	lws_start_foreach_dll_safe(struct lws_dll2 *, p, p1,
+				   builder.jobdir_hold_owner.head) {
+		saib_jobdir_hold_t *h = lws_container_of(p, saib_jobdir_hold_t, list);
+
+		if (saib_jobdir_is_held(h->vn))
+			n++;
+
+	} lws_end_foreach_dll_safe(p, p1);
+
+	return n;
+}
+
 void
 saib_jobdir_holds_destroy(void)
 {
diff --git a/src/builder/b-power.c b/src/builder/b-power.c
index 1c49793..0692dc4 100644
--- a/src/builder/b-power.c
+++ b/src/builder/b-power.c
@@ -591,6 +591,7 @@ saib_power_shutdown(void)
 int
 saib_reassess_idle_situation(void)
 {
+	unsigned int held;
 	char in_use = 0;
 
 	if (builder.stay) {
@@ -622,6 +623,18 @@ saib_reassess_idle_situation(void)
 		} lws_end_foreach_dll(d);
 	} lws_end_foreach_dll(mp);
 
+	held = saib_jobdir_holds_live();
+	if (held) {
+		/*
+		 * Tasks we started are between steps.  Going down would lose
+		 * their job dirs (a sai-virt VM's disk goes with it) and the
+		 * next step would come to a builder with no src/ tree.
+		 */
+		lwsl_notice("%s: %u job dirs held for started tasks\n",
+			    __func__, held);
+		in_use = 1;
+	}
+
 	if (builder.shell_owner.head) {
 		lwsl_notice("%s: builder has %d active shell sessions\n",
 			    __func__, builder.shell_owner.count);
diff --git a/src/builder/b-private.h b/src/builder/b-private.h
index d75d243..0971367 100644
--- a/src/builder/b-private.h
+++ b/src/builder/b-private.h
@@ -549,6 +549,8 @@ int
 saib_jobdir_is_held(const char *vn);
 void
 saib_jobdir_holds_destroy(void);
+unsigned int
+saib_jobdir_holds_live(void);
 
 /*
  * The job dir name for a task: the first 4 and last 4 chars of its uuid.  Both
diff --git a/src/builder/b-task.c b/src/builder/b-task.c
index bef6bed..7eb17ea 100644
--- a/src/builder/b-task.c
+++ b/src/builder/b-task.c
@@ -1567,6 +1567,20 @@ saib_consider_allocating_task(struct sai_plat_server *spm, lws_struct_args_t *a,
 			goto idle_decline;
 
 		lwsl_warn("%s: builder rejects offered task\n", __func__);
+
+		if (task->build_step > 0) {
+			char vn[16];
+
+			/*
+			 * It's a later step of a task we started, the server
+			 * keeps it for us and will offer it again.  Its job
+			 * dir isn't abandoned however long we keep saying not
+			 * yet, so don't let its hold lapse meanwhile.
+			 */
+			saib_task_jobdir_vn(vn, sizeof(vn), task->uuid);
+			saib_jobdir_hold(vn);
+		}
+
 		if (saib_queue_task_status_update(sp, spm, task, 0,
 						  SAI_TASK_REASON_BUSY)) {
 			lwsl_notice("TRAP: saib_queue_task_status_update failed (BUSY)\n");