It can take up to one year to conceive.
What you notice after sex is semen and contains very little sperm. It is mostly mucous. Most of the sperm has been deposited next to the cervix during ejaculation.
She needs to figure out her fertile time. Women are fertile about 2 weeks before their period. If her periods come at the same time every cycle then it should be simple to figure out. Good luck!
3 months is still way too early to be concerned! I would not say that she has a problem after such a short time. I think for most couples, around 80% conceive within 1 year of trying. For myself, it took 6 months for my first pregnancy (which ended in miscarriage) and then another 4 months to conceive again. But it's not at all unusual for conception to take 8 - 12 months as there's only a 15 - 20% chance each cycle. Don't stress about it so soon and please don't blame your wife or tell her she has a problem!
Also, you don't need to have sex every day, just the 3-4 days before she ovulates since sperm only survive for a few days. Your wife can use ovulation predictor kits to determine when she ovulates as it's different for every woman. I suggest the book "Taking Charge of Your Fertility" if you want to get a better understanding of how her cycle works.
Don't worry about semen dripping out -- assuming you have good sperm count, enough should be getting up there. I generally stayed on my back for 15 - 30 minutes afterwards, but honestly I don't think that really matters.
If you are still not conceiving after a year, then it's time to go to a fertility doctor to check both of you out.