Is there a certain month in pregnancy that women are more likely to smoke?

Yes. Most pregnant women will stop smoking by the end of their first trimester but resume after at some point after the baby is born. Pregnancy is an excellent me to kick the habit.
No. Actually, many women who smoke discontinue smoking while pregnant, but unfortunately the vast majority return to smoking after the baby is born. Very, very few women start to smoke or resume smoking during pregnancy, and I am not aware of any data on what stage of pregnancy women may return to smoking. Smoking is very bad for the fetus, and continued smoking around babies is bad for their health.