This is based on opinion. Please don't list it on a work's trope example list.
Tear Jerker / Prehistoric Park
The death of the mother Tyrannosaurus rex in "T-Rex Returns". Even Nigel seemed shaken by that.
Just before she died, the mother Rex let out one last defiant roar at Nigel, probably as a last-ditch attempt to protect her babies.
In "Dino Birds" Nigel is able to save several dinosaurs as the volcano in prehistoric China erupts. Unfortunately the Incisivosaurus he had encountered earlier was not among those dinosaurs saved.
Nigel and the popular big cat expert Saba Douglas-Hamilton mourning for sabretooth cats which suffer hunger and finally die because of starvation in "Saving the Sabretooth". And also the sad story of Martha the mammoth and her sister, even though it ends happily this time.
It looked like they were taking the animals from the times they were becoming extinct to not have as big an effect on the timeline... maybe.
During the episode "Saving the Sabretooth", the mother Ornithomimus rejects two of her eggs. Their retrieved and Bob tries to hatch them in an incubator. Soon all the other eggs hatch, but the two in the incubator don't, thankfully they do hatch eventually.
Matilda attacking and nearly killing her brother Terence in "A Bug House". It's never fully understood why exactly Matilda had become so hostile towards Terence either.