Why would a woman be able to conceive when she is in her 20's but unable in her 30's?

Several possibilitie: Salpingitis (tubal infection) could have intervened to render this woman infertile. Other possibilities: endometriosis, fibroids, premature ovarian failure. Talk with a reproductive endocrinologist if you have personal concerns.

Lots of reasons: Fertility can change drastically over 1-2 years much less 5-10. Women have fewer eggs and the ovaries may not function as well over time. A woman's fallopian tubes may be damaged over time. More eggs may be genetically abnormal. Or there can be changes in the sperm or the uterus. So your question addresses a very common occurrence.