How does further hybridization affect fertility?
Some first generation hybrids[f1] are viable and fertile, but when they mate with each other or back to either parental species[P}, the successive generations[f2] are sterile or feeble.  this concept is known as hybrid breakdown.  This is often seen in hybridized forms of domestic crops.  I am aware that some female tiger/lion hybrids are fertile, but I'm unaware of successful breeding of the f2 generations.  It could be a case of hybrid breakdown.

Article about hybrid breakdown in rice

Hybrid breakdown in Cichlid Fish