I'm sorry that your kitten is having this problem! There are a number of different things that could cause it, but these are the ones that come to mind first:
1. MOST LIKELY cause would be Parasites.
It's great that she is being dewormed routinely with the Anthelban. That medication is effective against hookworms and roundworms which are the most common intestinal parasites in kittens.
However, blood in the stool of a kitten is very often caused be COCCIDIA which is another type of parasite. It is a protozoan organism (like what causes Traveler's Diarrhea). It can be treated with a course of S-125/Albon medication.
Here is more about this problem:
2. Dietary indiscretion:
With a kitten, one always has to consider dietary indiscretion (garbage gut) since they are so curious they will eat just about anything. So, he might have eaten some dust bunnies, or a spider, or just about anything.
3. Viral infection:
A virus that causes diarrhea in kittens is Coronavirus. This seems unlikely because he is active and energetic. If he had this, treatment is supportive - meaning that it is aimed at maintaining hydration and preventing bacterial infections.
There is one form of Coronavirus that carries a poor prognosis and that is Feline Infectious Peritonitis. Your kitten sounds too energetic to have this serious infection, thankfully.
4. A bacterial infection:
Kittens can be affected by overgrowths of bacteria in the intestines. In an adult cat these might not be more than a nuisance, but in a kitten they can be serious. The 3 most common are Campylobacter, Salmonella and E.Coli.
Here is a link with more information:
In summary, there are a number of different problems that could be causing your kitten to have blood in the stool. **The top of my list would be Coccidia** The standard roundworm/hookworm dewormer will not treat this. However, it responds quickly to treatment with a medication that is given daily for 5 days. I would strongly recommend you take him in to see a veterinarian today, and take along a fresh stool sample.
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If you need more information, just click on reply and I will still be here to answer further questions.
The above is given for information only. Although I am a licensed veterinarian, I cannot legally prescribe medicines or diagnose your pet's condition without performing a physical exam. If you have concerns about your pet I would strongly advise contacting your regular veterinarian.
Best wishes to you and to your kitten!