Yes, you are describing the way the software works - if you indicate that you had different types of HDHP coverage at different times in the year, TurboTax expects you to enter each month anew. It obviously does not need to do this if you check that you had Family or Self-only coverage all year.
You say that your balance owed increases every time you reopened your return. Without going into your return (i.e., don't enter the interviews), please view your 1040 and see what changed so that we can track down the source of the change.
If you are using TurboTax desktop, go in Forms mode (upper right).
If you are using TurboTax Online, please see this FAQ for how to see your 1040 and Schedules 1, 2, and 3.
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