The question of what to reinsure has to be considered from both the insurer's and reinsurer's perspectives.
Reinsurance replaces the risk of an uncertain large payout, with a certain low payout. The insurer must decide how much of that certain payout to accept in return for avoiding the risk of large payouts. That is, the decision to reinsure is a question of how much risk to cede/retain based on financial management of the trade-off between reinsurance cost and the risk of pay out fluctuations.
In deciding how much cover to offer, the reinsurer faces the same issues that determine whether an insurer's risk is reinsurable as the insurer faced in the original contract with the individual. Quite simply, if a risk is insurable it is reinsurable.
Tension in the reinsurance decision making process arises because, in practice, decisions on insurability are made for non-underwriting reasons — for example, market building and political reasons. Therefore, the reinsurer needs access to the data on which the original insurance decision was made.
If that data is not available, the reinsurance market can fail to offer reinsurance, not because they risk is intrinsically not reinsurable but because the default decision is to not reinsure. This default is to err on the side of caution.