var ItemFlags: array of boolean;
...
begin
  SetLength(ItemFlags, Count);
  for i:=0 to count-1 do  ItemFlags[i]:=0;
  try
    try
      for i:=0 to count-1 do begin
        Items[i].BeforeRefresh;
        ItemFlags[i]:=true;
      end;
    finally
       BroadcastRefrech;
    end;
  finally
    for i:=0 to count-1 do
    if ItemFlags[i] then
    try
      Items[i].AfterRefresh;     
    except
      //Здесь нужно обработать исключение
    end;
  end;    
end;
А вообще нужно над архитектурой подумать.

SetLength(ItemFlags, Count);
      for i := 0 to Count - 1 do
        begin
          ItemFlags[i] := True;
          try
            Items[i].BeforeRefresh;
          except
            ItemFlags[i] := False;
            // Здесь нужно обработать исключение
          end;

type
  THolder=class(TInterfacedObject)
  private
    FObj: TItemClass;
  public
    constructor create(AObj: TItemClass);
    destructor destroy; override;
  end;

constructor THolder.create(AObj: TItemClass);
begin
  FObj:=AObj;
end;

destructor THolder.destroy;
begin
  try
    FObj.AfterRefresh;
  except
  end;

  inherited;
end;


procedure DefineHolder(AObj: TItemClass; out Holder: IUnknown);
begin
  try
    AObj.BeforeRefresh;
    Holder:=THolder.create(AObj);
  except
  end;
end;


//вызывалка
var Holders: array of IUnknown;
...
begin
  SetLength(Holders, Count);
  for i:=0 to count-1 do DefineHolder(Items[i], Holders[i]);
  BroadcastRefresh;
end;