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Tina,
There are three issues needed for pregnancy to occur:
I am afraid that your husband's sperm count is quite low. This is common after a vasectomy. A good sperm count should be between 40 to 60 million sperms per ml. Less than 20 million is generally considered low although pregnancy is still possible. A sperm count less than 10 million is quite low and needs further investigation.
In your case, taking alcohol at 1 drink 3- 4 nights a week should not affect your chances of pregnancy. And since you have not been on birth control pills for 3 years and you are ovulating as per the ovulation tracking tests, the only other thing you need to test for is patency of the tubes.
Please consult an infertility specialist. You will need to get a test called Hysterosalpingography (HSG) to test for patency of the tubes, and your husband will need tests to identify if the vasectomy is the cause of his low sperm count.
You can read about the various tests necessary in males and females in investigating infertility here:
I hope this helps.
Please feel free to ask a follow-up question if you wish to know more.
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