There are a couple of factors that influence how strong or weak a force in the chart the ascendant may be. Firstly, it is generally believed that the closer towards the beginning of the sign the ascendant falls, the stronger it will be. This is because most of the first house will fall into that sign. If the ascendant falls late in a sign, most of the first house will fall into the following sign, and thus weaken the effect of the ascendant's power. In addition the ascendant is thought to be stronger in influence when the sun is in a weak position in the chart. For example, it is traditionally believed that the sun is in a weaker position when it is placed at the bottom of the chart, near the immum coeli or IC. This is because the sun was literally on the other side of the earth when the subject was born, hidden from view. The sun may also be weaker in influence if it is unaspected, in other words if it forms no strong aspects or connections to the other planets.
Another factor concerning the effect of the ascendant is the theory that people become more like their sun sign after around 29 years old, as they grow older and more confident and thus have less of a need to present a public face to others. It is also theorised that when the progressed ascendant moves into the following sign, it weakens the influence of the natal ascendant.