[SalesForce] == condition is not working in rendered attribute of

There are 2 issues:

1) You have an extra 's' in the parameter that you're passing to the doChange function. Change the line to :

<apex:inputField value="{!opportunity.StageName}" onchange="doChange(this);"/>

2) You are toggling the visibility of the child element of the div(id="myId"), but the div itself remains hidden all the time. If the parent is hidden the child elements will always remain hidden regardless of their visibility setting.

So change the doChange function:

function doChange(thiss){
   if(thiss.value=='Closed Lost'){
      document.getElementById("myId").style.display='block';
   }else{
      document.getElementById("myId").style.display='None';
   }

}

Referring to the Reference apex:actionSupport, an example can be constructed:

For the example, make sure to give the VF Page a valid Opportunity Id like

apex/testPage?id=006i000000NMz1k

Controller:

    public class OpportunityExtension {

    public String reasonForLoss {get;set;}
    public String lostToWhom {get;set;}
    public String competitorsPrice {get;set;}
    public String competitorsMT {get;set;}

    public Opportunity opp {get;set;}

    public OpportunityExtension(ApexPages.StandardController sCon) {
        Id oppId = sCon.getId();
        if(oppId != null){
            this.opp = [SELECT Id, Name, StageName
                        FROM Opportunity
                        WHERE Id = :sCon.getId()
                        LIMIT 1];
        }
    }


    public void updateStageLossDetail(){
        if(opp.StageName != 'Closed Lost'){
            this.reasonForLoss = '';
            this.lostToWhom = '';
            this.competitorsPrice = '';
            this.competitorsMT = '';
            return;
        }
        this.reasonForLoss = 'Whoops';
        this.lostToWhom = 'The other guy';
        this.competitorsPrice = 'Way to low';
        this.competitorsMT = ':<';
    }
}

VF Page:

<apex:page standardController="Opportunity" extensions="OpportunityExtension">
    <apex:form >
        <apex:pageBlock >
            <apex:pageBlockSection columns="2">
                <apex:outputPanel >
                    <apex:inputField value="{!opp.StageName}"/>
                    <apex:actionSupport event="onchange" 
                                        action="{!updateStageLossDetail}" 
                                        rerender="StageLossDetail"/>
                </apex:outputPanel>
                <apex:outputPanel id="StageLossDetail">
                    <apex:pageBlockSection columns="2">
                        <apex:inputText value="{!reasonForLoss}"  label="Reason For Loss"/>
                        <apex:inputText value="{!lostToWhom}" label="Loss to Whom"/>
                        <apex:inputText value="{!competitorsPrice}" label="Competitor's Price"/>
                        <apex:inputText value="{!competitorsMT}" label="Competitor's MT"/>
                    </apex:pageBlockSection>
                </apex:outputPanel>
            </apex:pageBlockSection>
        </apex:pageBlock>
    </apex:form>
</apex:page>