A few things I've found:
IMPERFORATE ANUS (ARTRESIA ANI)
This is the absence of an anus. It may just be the anus that is occluded (obstructed or does not have an external opening) or the entire rectum may be missing. Sometimes the anus is present, but does not connect to the end of the bowel. Imperforate anus means the kitten cannot defecate, or cannot defecate normally since the lower bowel may open into another orifice. Symptoms akin to constipation occur and visual inspection may show lack of an anus. If the kitten is being reared by its mother, it may be several weeks before its condition is noticed. If it is being hand-reared, you will soon notice a problem. This condition can create a swollen stomach, or pot-belly appearance. Sometimes a Partial Blockage occurs, where some stool is released but some is retained within the body cavity.
As soon as the condition is discovered, seek veterinary help. If the anus is just blocked or doesn't connect to the bowel, it may be possible to correct this surgically. Surgery must be performed immediately to prevent or relieve constipation. If a larger portion of the bowel is missing, euthanasia is recommended. If the kitten survives surgery (surgery on tiny kittens is risky), the prognosis is good though it may be some time before it gains proper control over its bowel motions and it may need to be manually expressed for a while.
This is generalised infection i.e. the kittenâ€™s system is filled with harmful bacteria. It may have picked up these bacteria in the womb, during birth or after birth through a skin lesion or umbilical cord. Kittens with septicaemia have a raised temperature and their gums and tongue are fiery red. They are distressed, restless and often keep rolling over where they lie. They cry with a pathetic â€˜mew". Early diagnosis and prompt treatment are essential if the kitten is to survive. The vet will prescribe appropriate antibiotics. Such kittens are critically ill and require tube-feeding and attention to the environmental temperature. Many will not survive despite best efforts of vets.
Intestinal parasites (roundworms, tapeworms) are common in kittens unless the mother was wormed before pregnancy began. With abandoned kittens it is impossible to know whether the mother was wormed or not. Feral kittens almost always harbour worms.
Healthy kittens should be wormed with a preparation recommended by your vet when they reach 5 weeks old. Thereafter they should be wormed as advised by your vet until they reach 6 months old and are wormed routinely as adults.
Sick kittens or kittens under 3 weeks old should only be wormed under veterinary supervision e.g. if they have a severe worm burden which is compromising their health and growth.
Before each dosing the kittens should be accurately weighed, since too little wormer will be ineffective and too much may cause illness. In many kittens the worms cause no clinical signs. In others they can result in poor body condition, soft or bloody stools, loss of appetite, pot-belly and weight loss.
Some worms can be transmitted through the stools of infected cats, while others are carried by fleas. As well as worming, good hygiene and flea control are essential.
A general term for abdominal pain. Classic colic in infants is usually caused by an accumulation of gas in the stomach which causes the abdomen to swell. Gas trapped further along is "trapped wind" and causes similar pain. The abdomen becomes hard and bloated and the kitten shows signs of distress which may agitate the mother. Colic may be caused by overfeeding, bacterial infection, incorrect milk mixture, feeding too fast.
Because the mother becomes distressed, remove the kitten from the nest to treat it. Abdominal pain will be eased by releasing the gas build-up. Gently stroke the abdomen with warm damp cotton wool until the gas is released from one or other end of the kitten. If the gas is not released, seek veterinary help. The kitten should be fed little and often once it recovers. If it is prone to colic it may need preventative measures e.g. 0.5 ml Asalone (from chemists) 30 mins before feeding.
If all kittens in a litter are colicky, there is a problem with the mother's milk. Some mothers produce too strong milk. Antibiotics given to the mother can cause colic in the kittens. In these cases, hand-rearing is necessary.
Gastro-Enteritis is a serious inflammation of the stomach and intestine which causes abdominal pain, severe diarrhoea and often vomiting. It quickly causes dehydration and electrolyte loss due to excessive fluid loss. The kitten may cry in pain if it has the strength to do so. Seek immediate veterinary help. Antibiotics may be required to combat infection. If and when the condition stabilises, the kitten may be too weak to suckle and may require tube-feeding.
Feline Infectious Enteritis is a major killer of feral and stray kittens and a hazard in cat rescue/shelter situations. Care must be taken to avoid cross-infection.
I think that Colic is the most likely culprit here. It can be caused by formula that is too rich for the kitten, so it sometimes happens with hand-reared kittens. Try feeding less food, but more often.
I found this information here: http://www.messybeast.com/handrear.htm