In Oklahoma/Texas and a few of the surrounding states, I recommend that you should keep them on a preventative year round. We just do not get cold enough winters to kill fleas/ticks. Remember, fleas can live inside your house! So, you could have fleas year round. We want to “prevent” ever seeing any fleas/ticks! If you don’t see any on your pet it means that the product is working.
The best thing to do in this situation is to take your cat to your veterinarian. Cats are very different than dogs in the fact that cats tend to hide their symptoms for a longer period of time. It is also easier to notice when a dog goes a day without eating whereas a cat may go several days without eating before you realize it, which could increase the severity of whatever is ailing them. Always ere on the side of seeing the vet when your pet isn’t exhibiting normal behavior.