I'm flustered, can't understand why this won't work...  help please.

Here's my code, it works fine like this but I want to add an update to the event survey_sent__c field so that once the email is successfully sent the flag on the event that triggered this action is updated.  I want to do this to eliminate the recursive trigger.  Also, when the survey is actually completed the event gets updated again and I want to insure another message isn't sent.

public with sharing class SurveyEmail {
//
// this is called from a before update trigger by SurveyEmail.checkEvents(Trigger.new);
// 
    public void checkEvents(Event[] ev){

        List<Id>EventMembers = new List<Id>();
        Map<Id,Id> EventMap = new Map<Id, Id>();

        If (ev!=null){
            For (Event e:ev){
                if(e.Send_Survey__c==true && e.Event_Status__c=='Completed' && e.survey_sent__c==false){  // if e.survey_sent__c is true then abort
                    System.debug('#####  Survey box checked, processing Event with ID = ' + e.id);
                    If(e.WhoId != null){
                        EventMembers.add(e.WhoId);
                        EventMap.put(e.whoid, e.id);
e.survey_sent__c = true;    // tried this with the update statement at the end and it won't work - also tried creating a 2nd list and updating that, also fails
                    }
                }
            }
        }
If(EventMembers.size()>0){
            string EmailFailure=null;
    // generate list of contacts to send message to  
            System.debug('##### Creating List of Contacts to send message too... '); 
            List<Contact>myRecipients = [SELECT id, firstname, lastname, email FROM contact WHERE id IN :EventMembers AND (NOT email LIKE '%forbidden%') ];
   
    // create email objects as a list
            System.debug('#####  Creating list of messages ...');
            List<Messaging.SingleEmailMessage> allMsg = new List<Messaging.SingleEmailMessage>();
            OrgWideEmailAddress owa = [SELECT id, DisplayName, Address FROM OrgWideEmailAddress WHERE DisplayName='Global Sender' LIMIT 1];
            // append new message to above list for each Contact
            For (Contact c:myRecipients){
                Id EvId = EventMap.get(c.id);
                String theMsg = ('Please click the link below, or copy and paste into your browser to complete a brief survey ');
                theMsg = theMsg + ('related to your recent interaction with an awesome service representative. \n \n ');
                theMsg = theMsg + ('http://www.thethirdparty.com/survey?iv=############&q1=' + EvId + '&q2=' + c.id);
                                   
                System.debug('#####  Creating an instance of the message ...');
                try{
                    Messaging.SingleEmailMessage mail = new Messaging.SingleEmailMessage();
                    mail.setSenderDisplayname(owa.DisplayName);
                    mail.setReplyTo(owa.Address);
                    mail.setTargetObjectId(c.id);
                    mail.setUseSignature(false);
                    mail.setSubject('Please complete this survey from the company.');
                    mail.setPlainTextBody(theMsg);
                    mail.setSaveAsActivity(true);
                    System.debug('#####  Sending message ...');
                    Messaging.SendEmailResult[] mailResult=Messaging.sendemail(new Messaging.SingleEmailMessage[]{mail});
                    Messaging.sendEmail(new Messaging.SingleEmailMessage[] {mail});
                   
               
                    if (!mailResult[0].isSuccess() ){
                        EmailFailure = 'Email Failed: ' + mailResult[0].getErrors()[0].getMessage();
                    }
                }
                catch(Exception Exp){
                    EmailFailure='Exception: ' + Exp.getCause();
                }
            }
        }
    }
}