diff --git a/admin/tool/task/renderer.php b/admin/tool/task/renderer.php
index a25f3117e2f..f61909d256a 100644
--- a/admin/tool/task/renderer.php
+++ b/admin/tool/task/renderer.php
@@ -119,7 +119,9 @@ class tool_task_renderer extends plugin_renderer_base {
 
                 // Prepares the next run time cell contents.
                 $nextrun = '';
-                if ($stats['due'] > 0) {
+                if ($stats['stop']) {
+                    $nextrun = get_string('never', 'admin');
+                } else if ($stats['due'] > 0) {
                     $nextrun = get_string('asap', 'tool_task');
                 } else if ($stats['nextruntime']) {
                     $nextrun = userdate($stats['nextruntime']);
@@ -271,7 +273,11 @@ class tool_task_renderer extends plugin_renderer_base {
             if (!$started) {
                 $nextruntime = $task->get_next_run_time();
                 $due = $nextruntime < $now;
-                $nextrun = $due ? userdate($nextruntime) : get_string('asap', 'tool_task');
+                if ($task->get_attempts_available() > 0) {
+                    $nextrun = $due ? userdate($nextruntime) : get_string('asap', 'tool_task');
+                } else {
+                    $nextrun = get_string('never', 'admin');
+                }
 
                 if ($wantruntasks && ($faildelay || $due)) {
                     $nextrun .= ' '.html_writer::div(
diff --git a/lib/classes/task/manager.php b/lib/classes/task/manager.php
index 9d4a9e8dd63..b57fd17922f 100644
--- a/lib/classes/task/manager.php
+++ b/lib/classes/task/manager.php
@@ -543,6 +543,7 @@ class manager {
                     'failed' => 0,
                     'running' => 0,
                     'due' => 0,
+                    'stop' => false,
                 ];
             }
 
@@ -564,6 +565,11 @@ class manager {
                 }
             }
 
+            // Mark the task as stopped if it has no attempts available.
+            if (isset($r->attemptsavailable) && $r->attemptsavailable == 0) {
+                $classsummary['stop'] = true;
+            }
+
             $summary[$r->component][$r->classname] = $classsummary;
         }
         return $summary;