It depends of various factors. You would have to determine the stats for how often you get series of winners and series of losers, and how long those strings are on average. Generally though, I believe if you are going to trade a system mechanically like that, you have to take every signal, because you will generally never know which next trade will be a loser or a winner, and the moment you start cherry picking, you invalidate the stats that you derived.
Also depends on the characteristics of the system. For a trending system that generally averages 4 trades per day, then with the stats you mentioned, then I would consider stop trading if I get 3 trades in a row. But if that system generally produces 20 trades per day, then I would not stop after 3 winning trades.
I think the proper way to handle a system with the characteristics you mentioned, is to try to improve it with money alternative management techniques.
Please, be indulgent with me: this is my first post and English is not my mother language.
It's possible, but only if exist some scheme in time series of signs of trade return.
I think Wald-Wolfowitz test ( Runs Test) can help you. You can find info searching on wikipedia
For example, you consider daily returns of SP500 (yahoo data, ^GSPC) of last 20 years.
Math expectancy of daily return is close to zero:about 0.03% , probability of an up day is close to fifty-fifty: about 53%
Runs Test applied to signs of daily return gives:
Standard Normal = 1.9984, p-value = 0.04567.
Low p-value tell us that signs of return have (had..) some form of mean-reverting: more signs in row are negative, more probability to get an up day tomorrow.
Betting $100k on SP500 for one day, your expected profit (w/o transaction costs):
P/L # trade # trade positive
All days : $30 5020 53.5%
After a down day : $64 2329 54.9%
After 2 down days : $99 1047 55.5%
After 3 down days : $220 464 61.1%
After 4 down days : $308 169 63.1%
Equity-line in case 3 down days in row (w/o costs and w/o compounding profit) shows nice regularity of this market anomaly durig last 20 years.
However this is a rudimental analysis: correct test involves use of log return and must take in account risk (variance of expected log returns).
Obviously by now it is possible that the rule might be appropriate. But it might also just be an illusion of our brain's pattern finding networks. If you post an outline of the strategy or perhaps 20 example trades without information about the process then it might be possible to evaluate if serial correlation was likely or the rule was based on superstition. Otherwise this is interesting but essentially hollow speculation.