There have been no studies that I am aware of and history seems to indicate that there is not a correlation between longevity and frequency of wars.
Whether or not a nation goes to war is dependent on many factors that have nothing to do with a given ruler's age. A decision to go to war can be based upon being attacked by another nation, desiring natural resources, desiring territory in dispute, an overabundance of resources in the home country, a lack of political stability, etc.
The point is that the external, and internal, factors that work against a ruler/nation exist regardless of the ruler's age. I suppose you could find examples that a young ruler would invite an attack from a neighboring country, and conversely a weak and sick ruler. However, these instances are probably the exception to the rule.
The society's rules of succession, or existing legal framework, are a much better indicator of its proclivity for war. If there are not clear rules for succession you are more likely to have civil war. Likewise, if the elections of a country are a source of controversy you are more likely to have a civil war. Looking at resources, if a country has all the resources it needs it will probably not go to war. If that country has an economic boom and needs new markets for its wares it is more likely to engage in war to seek out colonies to peddle its wares, etc.