Why do the power and popularity of political parties change over time

They change for various reasons. One of them can be that they cannot deal with losing an election. Many times it happens that when a party loses an election it falls into disarray and does not have the strength or support to stay strong until the next elections where they might get a victory so the next election also becomes easily won by the winning party.

Another can be that new things in the world show up and the parties can't deal with it. For example, the populist party was very powerful in the United States but only for a specific amount of time when the problem they wanted to solve was a big issue. When the problem got resolved, the party more or less lost its platform and the smaller segments of the party were adopted by other parties leading to its complete weakening.

On the other hand, a party that's in the opposition can get a low of power and popularity if they manage to offer a solution to a problem. For example, Roosevelt offered a way to solve the great depression with his new deal and people believed him so the party got a lot of power, especially after he actually managed to solve it. 

How a party's position in society and its popularity and power changes depends on the spirit of the age and parties have to adapt to the cultural and social changes in the society if they want to stay strong. An example of this can be the Democratic party in the US. In the Civil War era, the democratic party was secessionist and supported slavery and was strong in the southern states. Nowadays, the Democratic party is the complete opposite of that because they changed their ways and got immense support from progressives.