So, I have been really getting into early European history and, through this, I noticed that both of these families seemed to whittle down to nothing fairly quickly after losing power. Is it known whether the two families were actively discouraged from having children or was it some other reason for the dying out of the dynasties?
Well, it is important to note that many dynasties have died out, often after ruling for less time the Merovingians or the Carolingians.
I'm going to talk a bit about the Carolingians as I know more about them. First of all, their near extinction preceded their loss of power. Many Carolingians in the generation after Charles the Bald and Louis the German died very quickly, which culminated in Charles the Fat acceding to all the Frankish kingdoms and then being deposed by his nephew, Arnulf of Carinthia, the illegitimate son of Carloman of Bavaria. Once this happened, the other Frankish Kingdoms (besides East Francia) elected their own, non-Carolingian kings. The lack of effective and of-age male Carolingian leaders was the reason non-Carolingian kings were elected. Had the other sons of Louis the German, Charles the Fat and Emperor Lothar not died out, Carolingian rule would likely have endured. However, Arnulf's lack of support in the other kingdoms prevented him from succeeding to the entire empire. Once other Carolingians came of age and succeeded to West Francia, the family had lost its monopoly on kingship. They lacked to resources and the political support to achieve the same sort of hegemony they had once enjoyed, despite their royal title. Nonetheless, they were still kings until they died out (Charless III, Louis IV and Lothair). In East Francia, the last Carolingian -- Louis the Child, son of King/Emperor Arnulf-- died in 911.
So rather than losing power than dying out, the chronology was in fact a string of deaths followed by the accession of any unqualified Emperor to all the Frankish kingdoms, then a palace coup by an illegitimate nephew who was unable to establish his rule in much of the Carolingian empire. The resultant accession of non-Carolingian kings in 888 was not by choice, but due to the lack of acceptable candidates. On top of all this, weakened Carolingians continued to rule much of the former empire into the 10th century, though less effectively than in its 8th and 9th century heyday. It was in fact the extinction of the dynasty (different branches, and at different phases) that was the cause of all this.
Why was there such high mortality? It was in fact a variety of reasons. Louis the German's sons Carloman of Bavaria and Louis the Younger both died of some sort of stroke it seems. Emperor Louis of Italy (son of Emperor Lothar) was childless. Charles the Bald's son Louis the Stammerer fell ill and died, while in turn his sons Louis III and Carloman II died from accidents (one involving chasing a girl and hitting a doorframe, the other falling from a horse during a hunt). As you can see, there was a ride range of causes of death and chance played a large role.
In a wider context, the Carolingians and Merovingians both ruled for quite a long time. The Merovingians from the mid-late 5th century (depending on whether you'd like to count Clovis' father Childeric as a legitimate king of the Franks or not) until 751, and the Caroligians from 751 until 888 and then again in different kingdoms until 911 and 986. These are both relatively long periods of kingship. The Tudors reigned from 1485 until 1603 when Elizabeth I died. Capetians and the Valois both had longer reigns before dying out (987 to 1328 and 1328 to 1589), though of course in both cases being succeeded by cousins. The Ottonians reigned from 919 to 1024. Basically, dynasties die out. It's important to note that there was high mortality in the middle ages, and politics was extremely cutthroat so weak or young monarchs often lost power.
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