Can the mating of a couple with Rhesus positive and negative blood types result in miscarriage?
I want to know can +ve and -ve blood group of a couple could be a cause of miscarriage in pregnancy?


Yes. In extreme cases, it can. You are talking about Rh Incompatibility, and can become a big issue when the mother has Rh(-) blood and the father has Rh(+) blood (such as the case with your cousin and his wife).

What could have happened (but definitely won't say for sure) is that your cousin's wife had a natural miscarriage which exposed her to the Rh proteins of the child, and then the subsequent pregnancy had complications due to the previous exposure and mother's development of antibodies which lead to the second miscarriage. However, I am not a licensed physician and you should consult a physician before pursuing any sort of treatments!!!

Rh factor is the presence of surface proteins on Erythrocytes (Red Blood Cells or "RBC"). If Leukocytes (White Blood Cells - most commonly reported as "T-cells") encounter Erythrocytes that do not share the Rh factor of their host, then they can develop antibodies to it - which help identify Antigens (foreign proteins and molecules). Once the Antibodies have been generated the Immune System can attack any foreign Erythrocytes. 

In this way, the mother's Immune System can actually attack the RBCs of her child.

You can find out more here: http://kidshealth.org/parent/pregnancy_center/your_pregnancy/rh.html

And a few select quotations:


  Rh incompatibility usually isn't a problem if it's the mother's first pregnancy because, unless there's some sort of abnormality, the fetus's blood does not normally enter the mother's circulatory system during the course of the pregnancy...
  
  ...Other ways Rh-negative pregnant women can be exposed to the Rh protein that might cause antibody production include blood transfusions with Rh-positive blood, miscarriage, and ectopic pregnancy...
  
  ...Rh antibodies are harmless until the mother's second or later pregnancies. If she is ever carrying another Rh-positive child, her Rh antibodies will recognize the Rh proteins on the surface of the baby's blood cells as foreign, and pass into the baby's bloodstream and attack those cells. This can lead to swelling and rupture of the baby's RBCs. A baby's blood count can get dangerously low when this condition, known as hemolytic or Rh disease of the newborn, occurs.*


And you are correct that there is a treatment via injection, but the Doctor is also correct in that administering it past the first pregnancy does little for future fetuses:


  Today, when a woman with the potential to develop Rh incompatibility is pregnant, doctors administer a series of two Rh immune-globulin shots during her first pregnancy. The first shot is given around the 28th week of pregnancy and the second within 72 hours after giving birth. Rh immune-globulin acts like a vaccine, preventing the mother's body from producing any potentially dangerous Rh antibodies that can cause serious complications in the newborn or complicate any future pregnancies.


And the ultimate effects of missing the shots and having very unfortunate luck:


  Rh incompatibility rarely causes complications in a first pregnancy and does not affect the health of the mother. But Rh antibodies that develop during subsequent pregnancies can be potentially dangerous to mother and child. Rh disease can result in severe anemia, jaundice, brain damage, and heart failure in a newborn. In extreme cases, it can cause the death of the fetus because too many RBCs have been destroyed.


Is there a cure? No. Once the antibodies have been developed, the Rh(+) protein is known to the mother's Immune System. Nothing short of wiping out the mother's Immune System would act as a cure.

However, in extreme cases, there are treatments:


  If a doctor determines that a woman has already developed Rh antibodies, then the pregnancy will be closely monitored to make sure that those levels are not too high. In rare cases, if the incompatibility is severe and the baby is in danger, a series of special blood transfusions (called exchange transfusions) can be performed either while the baby is still in the uterus or after delivery.


But don't fret yet!

Rh surface proteins are determined by genetics, and each time a child is conceived there is a chance that the Rh protein will be (-) if the exact genotype of the (+) parent allows it. So if your cousin's wife were to get pregnant again (and each time she does) it's a chance that the Rh Incompatibility (aka - "Hemolytic Disease", aka - "Rhesus Disease") won't show up.

So there are some reasons to stay positive.