Thanks for posting your query on health care magic.
Normally, periods are expected in the last week of OC pills( placebo period)
Since your wife has not got her period, i suggest her to get a home pregnancy
test done to rule out pregnancy.
There could be contraceptive
failure due to excess vomiting
You can also get a transvaginal scan done to detect early pregnancy.
Consult a Gynecologist for further management.
Hope this helps.