I am trying to write a trigger on task that queries the subject, and if it is equal to "Requalify", find the related account and related opportunity and change the opportunity status to "Re-qualify". I have the below trigger, but it is not changing the opportunity status. Any help would be greatly appreciated!

trigger TaskSubject on Task (after update, after insert) {

set<id> accountIdSet = new set<id>();
//capture all the subject names in a set
//set<string> subjectName = new set<string>{'Requalify'};
map<id, list<opportunity>> opptyMap = new map<id, list<opportunity>>();
list<opportunity> updateOppList = new list<opportunity>();

//get those tasks where the tasks are related to account. Capture the account IDs in a set.
for(task t: trigger.new){
            string tempId = string.valueOf(t.WhatId);
    if(tempId.startsWith('001')){
        accountIdSet.add(t.whatId);
    }
}

//If we have any account IDs then get the associated opportuity and store the one account to many opportunity in a map<id, list<opportunity>>
if(accountIdSet.size()>0){
    for(opportunity opp:[select Name, stageName, accountid from opportunity where accountid IN :accountIdSet]){
        if(opptyMap.containsKey(opp.accountId)){
            list<opportunity> oppList = opptyMap.get(opp.accountId);
            oppList.add(opp);
            opptyMap.put(opp.accountId, oppList);
        }else{
            list<opportunity> newOppList = new list<opportunity>();
            newOppList.add(opp);
            opptyMap.put(opp.accountId, newOppList);
        }
    }
}

//If we get the opportunities then change the stage.
if(Trigger.isUpdate && opptyMap.size()>0){
    for(task t: trigger.new){

 //Check if the subject of the task is one among the set 
 //and also confirm that the subject has been changed.

        if(t.subject != trigger.oldMap.get(t.id).subject && opptyMap.containsKey(t.whatId)){

  //iterate thru the list of the opportunity associated with that account 
  //and check which of the opportunity contains the task subject in the 
   //opportunity name and update the stage to re-qualify

            for(opportunity oppty: opptyMap.get(t.whatId)){
               {
                    oppty.stageName='Re-Qualify';
                    updateOppList.add(oppty);
                }
            }
        }
    }
}
if(Trigger.isInsert && opptyMap.size()>0){
     for(task t: trigger.new){
            if(opptyMap.containsKey(t.whatId)){
                for(opportunity oppty: opptyMap.get(t.whatId)){
                   if(oppty.name.contains(t.subject)){
                      oppty.stageName='Re-Qualify';
                      updateOppList.add(oppty);
                   }
               }
            }
        }
    }
//update the oppties
if(updateOppList.size()>0){
    update updateOppList;
}
}