I highly doubt that sex every day would be the cause of a chemical pregnancy.
A chemical pregnancy is usually a chromosome defect in the baby that causes the body to terminate it before it gets too far. It can also be a progesterone issue (body doesn't produce enough, and thus results in a pregnancy loss) Sex every day wouldn't really have an impact on either of those factors. (Obviously, there are more factors, but I'm just saying main ones for CP).
For both my pregnancies (both worked on first try), we did every day of the fertile windows. Most people I know also did that. It also depends on some people (some, the husband doesn't have infertility, but might produce less sperm, etc.). So really, both ways work (every day, every other day) it depends also on both your fertilities and so many other factors.
But whichever you choose wouldn't affect if you have a chemical pregnancy or not.