I went through the same thing. Lost 4 before 6 weeks after having 3 healthy pregnancies. Last one this past February. My Dr suggested the genetic testing as well, but before I could get the tests done I found out I was pregnant again...now 12w2d!! I still don't understand why they happened but I'm enjoying this pregnancy no matter what!
So sorry for your losses- it's never easy to go through a miscarriage, and I think it's even harder to not know why it happened.
Mostly, they run "blood work tests"- to test things like your thyroid, hormone levels, genetics, etc. The risk of miscarriage also increases after 35.
has your doctor given you any options for testing?