This is a good question, and the answer has two parts. First, let's address the concept underlying the strategy to which you are referring, and then discuss the validity of this strategy.
Buying more shares at a lower price than what you previously paid is known as averaging down, or decreasing the average price at which you purchased a company's shares. For example, say you bought 100 shares of the TSJ Sports Conglomerate at $20 per share. If the stock fell to $10 and you bought another 100 shares, your average price per share would be $15. Basically, you would be decreasing the price at which you originally owned the stock by $5.
However, even though your average purchase price would've gone down, you would've had an equal loss on your original stock - a $10 decrease on 100 shares renders a total loss of $1,000. Purchasing more shares to average down the price wouldn't change that fact, so do not misinterpret averaging down as a means to magically decrease your loss.
The trick is to know when to apply averaging down. But there are no hard-and-fast rules. Basically, you must re-evaluate the company you own and determine the reasons for the fall in price. If you feel the stock has fallen because the market has overreacted to something, then buying more shares may be a good thing. Likewise, if you feel there has been no fundamental change to the company, then a lower share price may be a great opportunity to scoop up some more stock at a bargain.
It's important to realize that it is not advisable to simply buy shares of any company whose shares have just declined. Even though you are averaging down, you may still be buying into an ailing company that will continue its downslide. Sometimes the best thing to do when your company's stock has fallen is to dump the shares you already have and cut your losses.