If you're Martingaling because you believe price always comes back to a certain level to give you a profit, then you don't use stops; you're averaging until price comes back. There is the possibility a trade may take you out of the game.
A trader I know once put a position on near the end of a day on an extremely overbought trending stock, looking for a nice pullback the next day. In pre-market the following morning price suddenly moved 50% against him in about 2 or 3 minutes on a news release. He was able to escape with a low six-figure loss. If he'd been Martingaling into the position as price trended strongly throughout that week and had on significantly more size than he had, there was a strong possibility the hard stop would've been his broker automatically liquidating his position and requesting additional margin to cover the rest of the loss his account couldn't cover.
Price itself signals reversals and there is no reason to average down unless you're managing such large sums of money that you have to average into and out of positions. Averaging down as trending instrument pulls back to the trend line is a commonly-used strategy. As far as I know, most institutional investors managing huge sums of money are trend followers, not counter-trend faders, though I'm sure there are plenty of hedge funds that employ the risky strategy. Whitney Tilson's fund had built a NFLX short into their largest short position over a period of time as the price just kept trending against them week after week. They covered a couple weeks ago not far from the all-time high (so far).
The easy money is made in the direction of a trend. Averaging up makes sense because you're using existing unrealized profits to leverage yourself in the direction of price movement.
Previous resistance in an uptrend tends to serve as support. Why? Because traders watching how nicely price broke through the previous resistance level prior to that, would like to buy somewhere near there or slightly higher, finding that to be a "safe" entry. If they buy near previous resistance, they are getting a "bargain" price in the trend and if the trend fails to hold up, they have a clean level at which to take a small loss and re-evaluate the price action for the next move.
If the trend resumes at that level and they then add to the winner as price breaks through the previous high, sure they've increased their cost basis, but they now have twice the size on in the direction of the move. If price pulls back down to the next "previous R becomes S" level, they look to add again and if the trend fails to hold there, they can exit for the profit on the original position and a small loss on the remaining positions, with the end result being a profit.
If price holds up there, they now have 3x size on as price moves to break the previous high again, which is how strong trends work and why it makes sense to add to winners rather than add to losers if you have a very large account to trade with.
