When a new row is added, the data from the other rows is cleared. How can I keep the previously entered data even if the entire table is rerendered.

Here is the code:

VF:

<apex:page standardController="Projects__c" extensions="addMultipleBurnsController" showHeader="true" sidebar="true">
 

 <apex:pageBlock title="{!Projects__c.Project_Name__c}" mode="maindetail">
     <apex:pageBlockSection title="Project Information">
         <apex:outputField value="{!Projects__c.Name}"/>
         <apex:outputField value="{!Projects__c.Project_Name__c}"/>
         <apex:outputField value="{!Projects__c.Status__c}"/>
         <apex:outputField value="{!Projects__c.Start_Date__c}"/>
         <apex:outputField value="{!Projects__c.Go_Live_Date__c}"/>
         <apex:outputField value="{!Projects__c.End_Date__c}"/>
     </apex:pageBlockSection>
     <apex:pageblocksection title="Project Details">
         <apex:outputField value="{!Projects__c.Sold_Hours__c}"/>
         <apex:outputField value="{!Projects__c.Goal_Hours__c}"/>
         <apex:outputField value="{!Projects__c.Planned_Hours__c}"/>
         <apex:outputField value="{!Projects__c.Pricing_Method__c}"/>
     </apex:pageblocksection>
 </apex:pageBlock>
 
 <apex:form >
 <apex:pageblock title="Add Multiple Burns">
     <apex:pageblockButtons >
         <apex:commandButton value="Save" action="{!save}" rerender="error"/>
         <apex:commandButton value="Add Row" action="{!addRow}" rerender="table,error" immediate="true"/>
         <apex:commandButton value="Remove Row" action="{!removeRow}" rerender="table,error" immediate="true"/>
     </apex:pageblockButtons>
     <apex:pageBlockTable value="{!burns}" var="a" id="table">
         <apex:column headerValue="Burn" width="125px">
             <apex:inputField value="{!a.Name}" required="true"/>
             <apex:inputField value="{!a.Burn_Status__c}"/>
         </apex:column>
         <apex:column headerValue="Resources" width="125px">
             <apex:inputField value="{!a.Resource_Type__c}"/><br />
             <apex:inputField value="{!a.Resource__c}"/>
         </apex:column>
         <apex:column headerValue="Dates Start/End" width="125px">
             <apex:inputField value="{!a.Start_Date__c}"/><br />
             <apex:inputField value="{!a.End_Date__c}"/>
         </apex:column>
         <apex:column headerValue="Hours Planned/Type" width="125px">
             <apex:inputField value="{!a.Hours_Planned__c}"/><br />
             <apex:inputfield value="{!a.General__c}"/>
         </apex:column>
         <apex:column headerValue="Details">
             <apex:inputField value="{!a.Burn_Details__c}" style="width:95%"/>
         </apex:column>
     </apex:pageBlockTable>
     
     <p><apex:pagemessages ></apex:pagemessages></p>
     
 </apex:pageblock>
 </apex:form>

</apex:page>

 Controller:

public class addMultipleBurnsController {
     
     //Class Variables
     public List<burn__c> burns {get; set;}
     private final projects__c proj;
     
     //Project Controller Extension
     public addMultipleBurnsController(ApexPages.StandardController stdController){
         this.proj = (projects__c)stdController.getRecord();
         burns = new List<burn__c>();
         burn__c theBurn = new burn__c();
         theBurn.Project__c = proj.Id;
         burns.add(theBurn);
         //burns.add(new burn__c());
     }
     
     public void addrow() {
         burn__c theBurn = new burn__c();
         theBurn.Project__c = proj.Id;
         burns.add(theBurn);
         //burns.add(new burn__c());
     }
     
     public void removerow(){
         Integer i = burns.size();
         burns.remove(i-1);
     }
     
     public pageReference save(){
         insert burns;
         PageReference back = new PageReference('/' + proj.Id);
         back.setRedirect(true);
         return back;
     }
     
}