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:
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:
And the ultimate effects of missing the shots and having very unfortunate luck:
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:
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.
To add a more concise answer:
Yes, the conflict between positive and negative Rh (Rhesus) blood groups can cause miscarriage.
The genetic makeup decides whether red blood cells (RBC) carry a specific surface protein known as Rhesus factor (Rh). If your own RBCs do not carry this protein (Rh-), your body will consider it (or RBC carrying it) a foreign substance and treat it like anything foreign - the immune system will respond and eliminate it, just like an infection.
If a Rh- mother has a child whose RBC are Rh+ (which is possible even if only one parent was Rh+), the mother's body will develop an immune response against the baby's blood itself.
This includes the immune response's memory: just like it remembers the "fake" infection from a vaccine to protect against a real disease, the immune system will remember the Rhesus protein, so if future pregnancies develop babies with Rh+ blood, the reaction will be more severe.