Averaging down in a losing position is a gamble where your entire capital is at stake.
Cutting losses with a stop is a professional discipline that preserves this capital for the hundreds of other opportunities that the market will inevitably provide.
Cut losses and let profits run. One successful trade with the right risk/reward ratio can cover several small stop losses. But one catastrophic trade that you 'averaged down to the bottom' can knock you out of the game for a long time, if not forever.
Take care of your capital. Follow the plan. Learn from history - both your own and Wall Street's. You are on the right track by asking such questions.
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