The response to this question will be different depending which of the investment philosophies you are using.
Value investors look at the situation the company is in and try to determine what the company is worth and what it will be worth in the future. Then they look at the current stock price and decide whether or not the stock is priced at a good deal or not. If the stock price is priced lower than they believe the company is worth, they would want to buy stock, and if the price rises above what they believe to be the true value, they would sell. These types of investors are not looking at the history or trend of what the price has done in the past, only what the current price is and where they believe the price should be in the future.
Technical analysis investors do something different. It is their belief that as stock prices go up and down, they generally follow patterns. By looking at a chart of what a stock price has been in the past, they try to predict where it is headed, and buy or sell based on that prediction.
In general, value investors are longer-term investors, and technical analysis investors are short-term investors.
The advice you are considering makes a lot of sense if you are using technical analysis. If you have a stock that is trending down, your strategy probably tells you to sell; buying more in the hopes of turning things around would be seen as a mistake. It is like the gambler in Vegas who keeps playing a game he is losing, hoping that his luck changes.
However, for the value investor, the historical price of a stock, and even the amount you currently have gained or lost in the stock, are essentially ignored. All that matters is whether or not the stock price is above or below the true value determined by the investor. For him, if the stock price falls and he believes the company still has a high value, it could be a signal to buy more. The above advice doesn't really apply for them.
Many investors don't follow either of these strategies. They believe that it is too difficult and risky to try to predict the future price of an individual stock. Instead, they invest in many companies all at once using index mutual funds, believing that the stock market as a whole always heads up over a long time frame. Those investors don't care at all if the prices of stock are going up or down. They simply keep investing each month, and hold until they have another use for the money. The above advice isn't useful for them at all.
No matter which kind of investing you are doing, the most important thing is to pick a strategy you believe in and follow the plan without emotion. Emotions can cause investors to make mistakes and start buying when their strategy tells them to sell.
Instead of trying to follow fortune cookie advice like "Don't throw good money after bad," choose an investment strategy, make a plan, test it, and follow it, cautiously (after all, it may be a bad plan).
For what it is worth, I am the third type of investor listed above. I don't buy individual stocks, and I don't look at the stock prices when investing more each month. Your description of your own strategy as "buy and hold" suggests you might prefer the same approach.