What happens if you don't follow thru on a check up after an abortion?

Maybe infertility. The reasons for a check up after an abortion are to make sure that you don't have an infection and that all the pregnancy tissue is gone. If you took your antibiotics, didn't have any significant pain, prolonged bleeding or fever and a urine pregnancy test is negative after 2-3 weeks, you may be ok to skip your follow-up. But make sure you're using birth control if you don't want to be pregnant.
Get follow up! It's the dependent on the type of abortion. If it's a medical abortion that you don't get follow up on, it's possibly that you may not know if the abortion was complete and so you may still be carrying a pregnancy or parts that may increase your risk of bleeding/infection later. Surgical abortions tend not to need follow up but both can be good for ensuring you get birth control afterwards!