Can you let me know how many times can a child with a low immune system catch the chickenpox?

Should be only one: By getting the chicken pox, one should produce immunity to the pox virus. If there is a second infection, it is probably reactivation of the virus and is called "shingles" or zoster infection. In any case, if your child has an immune problem, any infection is serious and you shold seek prompt medical attention by your pcp, specialty physician or other health care provider.

Generally once: In most cases, children only have chickenpox once, although some have a second, mild case. After that, the same virus is expressed as shingles.