No matter what your trading style or system parameters, failure to stick to these rules can cause significant damage to your equity. It is also just as dangerous to override a signal given, regardless of the reason.
Below is a chart of UK stock Electrocomponents, which had been in a slow uptrend for a while, until giving an exit signal last Wednesday. Failure to have acted on that signal could have meant losing all the profits gained over the preceding few weeks as the stock gapped down significantly on Friday.
Some people can develop issues where they have developed an emotional attachment to a position, particularly if they have held it for a while and it is in profit. In this business, you have to act in a dispassionate, unemotional manner. If you get an exit signal, act on it! So what if you think the stock is going higher - a systematic trend following method doesn't allow for opinions, it only reacts or generates signals based on price movement, which is the ONLY thing that can give you a profit or a loss.
In my own trading, I always place stops whenever I open a new position, and monitor and update these as required by the system rules. Therefore, I avoid this issue, in that the market itself takes me out of any positions - there is no scope for discretionary decisions. The market does not care whether I am long or short a stock, or whether I am in profit or loss. My stops are placed in accordance with my system rules, and if they get hit, they get hit.
If you are using a systematic approach such as a trend following system it is essential that you keep a review of your positions on a daily basis, as well as update your trading stops as the system requires. Otherwise, what is the point of having rules to follow if (for whatever reason) you don't implement them?