diff --git a/Common/src/Pollster/Pollster.cs b/Common/src/Pollster/Pollster.cs
index bf098cf3a..9467a034b 100644
--- a/Common/src/Pollster/Pollster.cs
+++ b/Common/src/Pollster/Pollster.cs
@@ -43,6 +43,8 @@
 using Microsoft.Extensions.Diagnostics.HealthChecks;
 using Microsoft.Extensions.Logging;
 
+using TaskStatus = ArmoniK.Core.Common.Storage.TaskStatus;
+
 namespace ArmoniK.Core.Common.Pollster;
 
 public class Pollster : IInitializable
@@ -170,12 +172,7 @@ public async Task Init(CancellationToken cancellationToken)
 
   public async Task<HealthCheckResult> Check(HealthCheckTag tag)
   {
-    if (healthCheckFailedResult_ is not null)
-    {
-      return healthCheckFailedResult_ ?? HealthCheckResult.Unhealthy("Health Check failed previously so this polling agent should be destroyed.");
-    }
-
-    if (endLoopReached_)
+    if (endLoopReached_ && taskProcessingDict_.IsEmpty)
     {
       return HealthCheckResult.Unhealthy("End of main loop reached, no more tasks will be executed.");
     }
@@ -234,6 +231,12 @@ public async Task<HealthCheckResult> Check(HealthCheckTag tag)
       healthCheckFailedResult_ = result;
     }
 
+    if (tag == HealthCheckTag.Liveness && taskProcessingDict_.Any(pair => pair.Value.GetAcquiredTaskInfoOrNull()
+                                                                              ?.TaskStatus is not null and not TaskStatus.Dispatched))
+    {
+      return HealthCheckResult.Healthy();
+    }
+
     if (tag == HealthCheckTag.Readiness && taskProcessingDict_.IsEmpty)
     {
       return HealthCheckResult.Unhealthy("No tasks to process");
@@ -264,11 +267,10 @@ await Init(exceptionManager_.EarlyCancellationToken)
         if (healthCheckFailedResult_ is not null)
         {
           var hcr = healthCheckFailedResult_.Value;
-          exceptionManager_.FatalError(logger_,
-                                       hcr.Exception,
-                                       "Health Check failed with status {Status} thus no more tasks will be executed:\n{Description}",
-                                       hcr.Status,
-                                       hcr.Description);
+          logger_.LogError(hcr.Exception,
+                           "Health Check failed with status {Status} thus no more tasks will be acquired (tasks already acquired will be executed to completion if possible):\n{Description}",
+                           hcr.Status,
+                           hcr.Description);
           return;
         }
 
diff --git a/Common/src/Pollster/TaskHandler.cs b/Common/src/Pollster/TaskHandler.cs
index cb6ae1329..0fbc7595a 100644
--- a/Common/src/Pollster/TaskHandler.cs
+++ b/Common/src/Pollster/TaskHandler.cs
@@ -707,12 +707,21 @@ await ReleaseAndPostponeTask()
   ///   The metadata of the task
   /// </returns>
   public TaskInfo GetAcquiredTaskInfo()
+    => GetAcquiredTaskInfoOrNull() ?? throw new ArmoniKException("TaskData should not be null after successful acquisition");
+
+  /// <summary>
+  ///   Get the meta data of the acquired task
+  /// </summary>
+  /// <returns>
+  ///   The metadata of the task or null
+  /// </returns>
+  public TaskInfo? GetAcquiredTaskInfoOrNull()
     => taskData_ is not null
          ? new TaskInfo(taskData_.SessionId,
                         taskData_.TaskId,
                         messageHandler_.MessageId,
                         taskData_.Status)
-         : throw new ArmoniKException("TaskData should not be null after successful acquisition");
+         : null;
 
   /// <summary>
   ///   Release task from the current agent and set message to <see cref="QueueMessageStatus.Postponed" />
diff --git a/Common/tests/Helpers/SimplePullQueueStorageChannel.cs b/Common/tests/Helpers/SimplePullQueueStorageChannel.cs
index ce3aee20e..8091c5bf4 100644
--- a/Common/tests/Helpers/SimplePullQueueStorageChannel.cs
+++ b/Common/tests/Helpers/SimplePullQueueStorageChannel.cs
@@ -32,10 +32,11 @@ namespace ArmoniK.Core.Common.Tests.Helpers;
 
 public class SimplePullQueueStorageChannel : IPullQueueStorage, IPushQueueStorage
 {
-  public readonly Channel<IQueueMessageHandler> Channel = System.Threading.Channels.Channel.CreateUnbounded<IQueueMessageHandler>();
+  public readonly Channel<IQueueMessageHandler> Channel     = System.Threading.Channels.Channel.CreateUnbounded<IQueueMessageHandler>();
+  public          HealthCheckResult             CheckResult = HealthCheckResult.Healthy();
 
   public Task<HealthCheckResult> Check(HealthCheckTag tag)
-    => Task.FromResult(HealthCheckResult.Healthy());
+    => Task.FromResult(CheckResult);
 
   public Task Init(CancellationToken cancellationToken)
     => Task.CompletedTask;
diff --git a/Common/tests/Pollster/PollsterTest.cs b/Common/tests/Pollster/PollsterTest.cs
index f9ea55cea..a1420cb08 100644
--- a/Common/tests/Pollster/PollsterTest.cs
+++ b/Common/tests/Pollster/PollsterTest.cs
@@ -376,7 +376,6 @@ await testServiceProvider.Pollster.Init(CancellationToken.None)
     // This test that we return from the mainloop after the health check is unhealthy
     await testServiceProvider.Pollster.MainLoop()
                              .ConfigureAwait(false);
-    Assert.True(testServiceProvider.ExceptionManager.Failed);
   }
 
   [Test]
@@ -449,10 +448,14 @@ await Task.Delay(TimeSpan.FromMilliseconds(delay_),
 
   [Test]
   [Timeout(10000)]
-  public async Task ExecuteTaskShouldSucceed()
+  public async Task ExecuteTaskShouldSucceed([Values] HealthStatus healthStatus)
   {
-    var mockPullQueueStorage    = new SimplePullQueueStorageChannel();
-    var waitWorkerStreamHandler = new SimpleWorkerStreamHandler();
+    var mockPullQueueStorage = new SimplePullQueueStorageChannel
+                               {
+                                 CheckResult = new HealthCheckResult(healthStatus,
+                                                                     $"value for test called {nameof(ExecuteTaskShouldSucceed)}"),
+                               };
+    var waitWorkerStreamHandler = new WaitWorkerStreamHandler(500);
     var simpleAgentHandler      = new SimpleAgentHandler();
 
     using var testServiceProvider = new TestPollsterProvider(waitWorkerStreamHandler,
@@ -480,8 +483,13 @@ await testServiceProvider.Pollster.Init(CancellationToken.None)
                              .ConfigureAwait(false);
 
     var stop = testServiceProvider.StopApplicationAfter(TimeSpan.FromSeconds(1));
+    var loop = testServiceProvider.Pollster.MainLoop();
 
-    Assert.DoesNotThrowAsync(() => testServiceProvider.Pollster.MainLoop());
+    // checking health should not interrupt task execution
+    var res = await testServiceProvider.Pollster.Check(HealthCheckTag.Liveness)
+                                       .ConfigureAwait(false);
+
+    Assert.DoesNotThrowAsync(() => loop);
     Assert.DoesNotThrowAsync(() => stop);
 
     Assert.AreEqual(TaskStatus.Completed,