What is BookMark Error in flex and how it is resolved?

folderObj.children is an ArrayCollection.

>> folderObj.children is an ArrayCollection
Good! Since an ArrayCollection extends ListCollectionView:

var res:ArrayCollection = event.result as  ArrayCollection;
if(folderObj.children != null) {
       var ac:ArrayCollection = folderObj.children as ArrayCollection;
       ac.disableAutoUpdate();
       ac.addItem(res[i]);
       ac.enableAutoUpdate();
}

folderObj.children.enableAutoUpdate();

same error is being shown in the above line.

Error: Bookmark no longer valid.
      at ListCollectionViewCursor/seek()[C:\autobuild\3.2.0\frameworks\projects\framework\src\mx\collections\ListCollectionView.as:2048]
      at mx.collections::HierarchicalCollectionViewCursor/get current()[C:\work\flex\dmv_automation\projects\datavisualisation\src\mx\collections\HierarchicalCollectionViewCursor.as:198]
      at mx.controls.advancedDataGridClasses::AdvancedDataGridBase/createRow()[C:\work\flex\dmv_automation\projects\datavisualisation\src\mx\controls\advancedDataGridClasses\AdvancedDataGridBase.as:1629]
      at mx.controls.advancedDataGridClasses::AdvancedDataGridBase/makeRowsAndColumns()[C:\work\flex\dmv_automation\projects\datavisualisation\src\mx\controls\advancedDataGridClasses\AdvancedDataGridBase.as:892]
      at mx.controls::AdvancedDataGridBaseEx/makeRowsAndColumns()[C:\work\flex\dmv_automation\projects\datavisualisation\src\mx\controls\AdvancedDataGridBaseEx.as:1918]
      at mx.controls::AdvancedDataGrid/makeRowsAndColumns()[C:\work\flex\dmv_automation\projects\datavisualisation\src\mx\controls\AdvancedDataGrid.as:7169]
      at mx.controls.listClasses::AdvancedListBase/makeRowsAndColumnsWithExtraRows()[C:\work\flex\dmv_automation\projects\datavisualisation\src\mx\controls\listClasses\AdvancedListBase.as:1231]
      at mx.controls.listClasses::AdvancedListBase/updateDisplayList()[C:\work\flex\dmv_automation\projects\datavisualisation\src\mx\controls\listClasses\AdvancedListBase.as:3501]
      at mx.controls::AdvancedDataGridBaseEx/updateDisplayList()[C:\work\flex\dmv_automation\projects\datavisualisation\src\mx\controls\AdvancedDataGridBaseEx.as:1778]
      at mx.controls::AdvancedDataGrid/updateDisplayList()[C:\work\flex\dmv_automation\projects\datavisualisation\src\mx\controls\AdvancedDataGrid.as:6007]
      at mx.controls.listClasses::AdvancedListBase/validateDisplayList()[C:\work\flex\dmv_automation\projects\datavisualisation\src\mx\controls\listClasses\AdvancedListBase.as:3072]
      at mx.managers::LayoutManager/validateDisplayList()[C:\autobuild\3.2.0\frameworks\projects\framework\src\mx\managers\LayoutManager.as:622]
      at mx.managers::LayoutManager/doPhasedInstantiation()[C:\autobuild\3.2.0\frameworks\projects\framework\src\mx\managers\LayoutManager.as:695]
      at Function/http://adobe.com/AS3/2006/builtin::apply()
      at mx.core::UIComponent/callLaterDispatcher2()[C:\autobuild\3.2.0\frameworks\projects\framework\src\mx\core\UIComponent.as:8628]
      at mx.core::UIComponent/callLaterDispatcher()[C:\autobuild\3.2.0\frameworks\projects\framework\src\mx\core\UIComponent.as:8568]
      at flash.events::EventDispatcher/dispatchEventFunction()
      at flash.events::EventDispatcher/dispatchEvent()
      at mx.collections::HierarchicalCollectionView/nestedCollectionChangeHandler()[C:\work\flex\dmv_automation\projects\datavisualisation\src\mx\collections\HierarchicalCollectionView.as:1202]
      at flash.events::EventDispatcher/dispatchEventFunction()
      at flash.events::EventDispatcher/dispatchEvent()
      at mx.collections::ListCollectionView/dispatchEvent()[C:\autobuild\3.2.0\frameworks\projects\framework\src\mx\collections\ListCollectionView.as:833]
      at mx.collections::ListCollectionView/addItemsToView()[C:\autobuild\3.2.0\frameworks\projects\framework\src\mx\collections\ListCollectionView.as:931]
      at mx.collections::ListCollectionView/listChangeHandler()[C:\autobuild\3.2.0\frameworks\projects\framework\src\mx\collections\ListCollectionView.as:1051]
      at mx.collections::ListCollectionView/handlePendingUpdates()[C:\autobuild\3.2.0\frameworks\projects\framework\src\mx\collections\ListCollectionView.as:1210]
      at mx.collections::ListCollectionView/enableAutoUpdate()[C:\autobuild\3.2.0\frameworks\projects\framework\src\mx\collections\ListCollectionView.as:370]
      at com.zetainteractive.model.managers::ListManager/sampleData()[D:\ZetaMail5\zetamail_flex\src\com\zetainteractive\model\managers\ListManager.as:2807]
      at com.cynergysystems.tango::GenericResponder/result()[D:\ZetaMail5\zetamail_flex\src\com\cynergysystems\tango\GenericResponder.as:22]
      at mx.rpc::AsyncToken/http://www.adobe.com/2006/flex/mx/internal::applyResult()[C:\autobuild\3.2.0\frameworks\projects\rpc\src\mx\rpc\AsyncToken.as:199]
      at mx.rpc.events::ResultEvent/http://www.adobe.com/2006/flex/mx/internal::callTokenResponders()[C:\autobuild\3.2.0\frameworks\projects\rpc\src\mx\rpc\events\ResultEvent.as:172]
      at mx.rpc::AbstractOperation/http://www.adobe.com/2006/flex/mx/internal::dispatchRpcEvent()[C:\autobuild\3.2.0\frameworks\projects\rpc\src\mx\rpc\AbstractOperation.as:193]
      at mx.rpc::AbstractInvoker/http://www.adobe.com/2006/flex/mx/internal::resultHandler()[C:\autobuild\3.2.0\frameworks\projects\rpc\src\mx\rpc\AbstractInvoker.as:193]
      at mx.rpc::Responder/result()[C:\autobuild\3.2.0\frameworks\projects\rpc\src\mx\rpc\Responder.as:43]
      at mx.rpc::AsyncRequest/acknowledge()[C:\autobuild\3.2.0\frameworks\projects\rpc\src\mx\rpc\AsyncRequest.as:74]
      at NetConnectionMessageResponder/resultHandler()[C:\autobuild\3.2.0\frameworks\projects\rpc\src\mx\messaging\channels\NetConnectionChannel.as:515]
      at mx.messaging::MessageResponder/result()[C:\autobuild\3.2.0\frameworks\projects\rpc\src\mx\messaging\MessageResponder.as:199]

What if you remove the enableAutoUpdate() and just keep the disableAutoUpdate()?

The objects are not getting added to the folderObj, if i remove enableAutoUpdate().

>> The objects are not getting added to the folderObj, if i remove enableAutoUpdate().
Well, they are but the view doesn't show them due to disableAutoUpdate() call as the Flex help states:

Prevents changes to the collection itself and items within the collection from being dispatched by the view. Also prevents the view from updating the positions of items if the positions change in the collection.

But the above is followed by:
The changes will be queued and dispatched appropriately after enableAutoUpdate is called.
The disableAutoUpdate method acts cumulatively; the same number of calls to enableAutoUpdate  are required for the view to dispatch events and refresh.

So, the question is: when calling enableAutoUpdate() again without having the problem...

how to find that ....by calling enableAutoUpdate() will not cause the problem....

It's clear that calling disableAutoUpdate() helps in avoiding the error.
Apparently calling enableAutoUpdate() is also needed if you want the view to be updated according to the changes.
But if you do at that point, you get the same error.
Maybe you should call it "later"...

Could you try this:

var res:ArrayCollection = event.result as  ArrayCollection;
if(folderObj.children != null) {
       folderObj.children.disableAutoUpdate();
       folderObj.children.addItem(res[i]);
       callLater(
           public function():void {
                folderObj.children.enableAutoUpdate();
       });
}

Compilation error is showing in the above code at callLater saying that "call to a possibly undefined method callLater".

Well, callLater() is a method that can be called on all objects that inherit from the UIComponent class.
I don't know the context of your code snippet.
I would suggest you call it on the "view class/control" that displays that collection.

Here the Problem is the code is in the Action Script File. How to deal with that in AS file

>> the code is in the Action Script File
I was already assuming that, yes.
My comment stays valid.

If you simply wrote callLater() in fact you call it on this, being the instance of the class your AS file represents.
That class should inherit from UIComponent.