There are several insects (as well as other wildlife) a plant can fall victim to when growing outdoors. Here you will find explanations of common pests and methods for repelling them.
Common Insects
Spider mites
Thrips
Common solutions
Neem oil
Neem oil can be added to feed water to repel insects such as spider mites or thrips. Be aware that it has a delayed effect and should be applied preventatively.
Predator insects
Its possible to add "good" insects that will hunt the insects you want to remove.
Some example predators for spider mites are Phytoseiulus persimilis and Amblyseius californicus.
For Thrips you might use Amblyseius cucumeris.