Hi Vishal Thats right. So since the job would be running every night or when ever it is going to email the respective PM and Director about the task near overdue. 

I have tried to modify the code further please have a look at it.

I didnt change much but has taken the condition out of query ..

global class EscalateAnnualEnrollmentTaskProcess implements Schedulable {
   global void execute(SchedulableContext ctx) 
   {
   List<Task> tasksnearoverdue = new List<Task>(); 
   DateTime Dt = System.today();
Date D = Date.newInstance(Dt.year(),Dt.Month(),Dt.day());
 
      /* list of open annual enrollment requests */
      List<Annual_Enrollment_Request__c> requestIds = [SELECT Id FROM Annual_Enrollment_Request__c WHERE status__c != 'ACCEPTED'];
      /* list of tasks associated with these requests near overdue activitydate - 2 */
      List<Task> tasksOverdue =[SELECT Id, ActivityDate, Subject FROM Task WHERE WhatId IN :requestIds AND IsClosed = false]; //AND ActivityDate <= :Date.today().addDays(-2) ] ;
      /* iterate over the tasks */
      for (Task t:tasksOverdue){
      
         if(t.ActivityDate.addDays(- 2)== system.today() )
                 tasksnearoverdue.add(t);
      }
      
      
      
      for (Task t:tasksNearOverdue) {
         /* lookup the object */
         Annual_Enrollment_Request__c request = [SELECT Id, Project_Manager__c, Director__c FROM Annual_Enrollment_Request__c WHERE Id = :t.WhatId];
 

         /* lookup the user and send the email*/
         User projectmanager = [SELECT Id, Name, Email FROM User WHERE Id = :request.Project_Manager__c];
         sendemail(projectmanager, t);
         /* lookup the user and send the email */
         User director =  [SELECT Id, Name, Email FROM User WHERE Id = :request.Director__c];
         sendemail(director, t);
      }
   
 } 
   global void sendemail(User u, Task t)
   {
      Messaging.SingleEmailMessage email = new Messaging.SingleEmailMessage();
      string[] toaddress = New String[] {u.Email};
      email.setSubject('Task Almost Overdue');
      email.setPlainTextBody(t.Subject + 'is due ' + t.ActivityDate + ' and needs some attention.');
      email.setToAddresses(toaddress);
      Messaging.sendEmail(New Messaging.SingleEmailMessage[] {email});
   }
}