Kite does allow you to do this but from a different point of view, the right point of view.
Lets assume you have bought a stock at Rs.100 in your Holdings. After a few days you see the stock price go to 120 so you sell it on that day in the morning. As of this sell trade, your stock is sold out from your Holdings.
Now on the same day in the afternoon, the same stock has fallen to 110 and you wish to buy it back and so you buy it back. So you have bought back the stock into your Holdings.
But how the system sees this is that you took a sell trade in the morning at 120 and you squared off this trade by buying it back at 110. So you make a Rs.10 intraday profit and the stock is still present in your Holdings at 100.
What you are saying is the holdings should be sold out at 120 and should be rebought back at 110(which will be the new buy price). But what happens in actuality is your Holdings remain at Rs.100 and you make a Rs.10 intraday profit which is the way the orders are processed at the exchange. The net effect is the same.