"To date" (meaning to be in a romantic relationship with) is an odd verb, because it involves an ongoing, evolving process. For this reason it is not natural to use the simple present, as in "I date her". Instead we use the present progressive "I am dating her".
Using the simple past indicates an end to the "dating period",
He dated her while she was in medical school (but they are not dating anymore).
He dated her while she was in medical school (then they got married).
If you want to talk about a past time where they were still dating, use the past progressive:
They were dating while she was in medical school.
This does not give any information whether or not they are still dating. It simply states a condition that was true at the time.
Finally, to indicate an ongoing condition that is still true now, you can use the present perfect progressive.
They have been dating ever since she started medical school.