Your logic is wrong .
Watch out LOC 30 to 31 in your code. here you are just copy pasting same X in all the project records. Single inset, update, delete should work finebutu thsi fails in mass udpate of childs which is expected. 

Also avoid using for inside a for loo LOC29 and 30. The code is too bad and would create issues (might be working ok for now)

You should create the MAP n all such cases
here is the updated code. i have not tested this but this should work. Let me know in case of any issues

<pre>
Trigger CountHours On Participants__c (After Insert, After Update, After Delete, After Undelete) {
    List<Participants__c> Parti = New List<Participants__c>();
    Set<ID> ProjIds = New Set<ID>();
    List<Participants__c> listTriggerParticipants;
    if (!Trigger.isDelete) {
        listTriggerParticipants = (List<Participants__c>)Trigger.New;
        /* for (Participants__c PC : Trigger.New) {
             ProjIds.add(PC.Project__c);
         }*/
    }
    else {
        listTriggerParticipants = (List<Participants__c>)Trigger.old;
        /* for (Participants__c PC : Trigger.old) {
             ProjIds.add(PC.Project__c);
         }*/
    }
    //Just one For Loop, removed redundancy
    for (Participants__c PC : listTriggerParticipants) {
        ProjIds.add(PC.Project__c);
    }
    /* Use AggregateResults Query instread of un-neccesary for loops
    Enhanced performace
    Parti = [Select Devoted_Hours__c From Participants__c where Project__c IN: ProjIds];
    Double X = 0;
    for (Integer I = 0; I < Parti.size(); I++) {
        if (Parti[I].Devoted_Hours__c != null) {
            X += Parti[I].Devoted_Hours__C;
        }
    }*/
    //Use meaningful names
    Double dDevotedHrs = 0;
    //use map to create rollup for each project record
    Map<Id, Double> mapDevotedHrPerProject = new  Map<Id, Double>();
    //new AggregateResult query
    for (AggregateResult ar : [Select Project__c, SUM(Devoted_Hours__c) totalDevotedHrs
                               From Participants__c
                               where Project__c IN: ProjIds
                               group by Project__c ])  {
        dDevotedHrs = Double.valueOf(ar.get('totalDevotedHrs'));
        mapDevotedHrPerProject.put(Project__c, dDevotedHrs);
    }
    //USe For loops
    //List<Projects__c> Projs = New List<Projects__c>([Select Total_Devoted_Hours__c From Projects__c Where ID IN: ProjIds]);
    List<Projects__c> listProjs = new List<Projects__c>();
    //Save SOQL here and juste uterate over the map at LOC 35
    For(String eachProjectID : mapDevotedHrPerProject.keySet() ) {
        Projects__c eachProject = new Projects__c(id = eachProjectID,
                Total_Devoted_Hours__c = mapDevotedHrPerProject.get(eachProjectID));
        listProjs.add(eachProject);
    }
    //This is not needed, as we already know what all project records need an Update.
    /*if (!Trigger.isDelete) {
        for (Participants__c Partici : Trigger.New) {
            for (Projects__c P : Projs) {
                P.Total_Devoted_Hours__c = X;
            }
        }
    }
    else {
        /*for (Participants__c Partici : Trigger.Old) {
            for (Projects__c P : Projs ) {
                P.Total_Devoted_Hours__c = X;
            }
        }
    }*/
    //use readbale names
    //update Projs;
    update listProjs;
}
</pre>