In the case of high inbreeding, which results in a genetic similarity of the clan to a large degree, in this case the difference resulting from the environment, as the quantitative traits are affected by both genetic and environmental factors
To avoid this, out-breeding of the herd must be brought about through mating (crossbreeding)
Traits which are mainly influenced by enviroment than additive genetic or breeding value in fact have low heritability like reproductive triats. So the reason of low heritabe is the nature of the triat in addition of data accuracy and using best fit model for estimation.
Low genetic variability- both additive genetic and non additive genetic. Happens during long selection experiments possibly reaching a selection plateau. Closed herd selection ( inbreeding) without access to outside source of mating, high environmental influences. Natural selective forces overcoming artificial selection practices. Randon breeding without artificial selection for 2 to 3 generations may break up linkages ,if any, to revive genetic variability, may help. The trait in question is generally lowly heritable. Size of the population is another factor for this situation
In my opinion, sheep is an animal that reacts very quickly to environmental conditions and therefore causes some of the traits in them to be more affected by environmental factors, and usually the heritability coefficient of these traits decreases.