The events are in the past, and the writer (who is the child involved) is looking back on them from a time well after the events. Thus "would remain" is chosen, to indicate that the concerns remained a hunch for a time period now long ended, specifically through the end of the pregnancy when the birth revealed the actual condition.
This form, with "would" followed by a present-tense verb, is used (among other purposes) to describe situations that existed for a time, but are now over, or a condition still existing, but regarded from a past moment. Often the ending time is indicated by "until" or a similar word, but that can be omitted, as it is here. This form is also used for a habitual past action.
- The problem would continue until we examined the valve.
- John would often ride his bicycle to work.
- After the glacier melted, the heap of stones it moved, known as a terminal moraine, would remain.
- While neither side agreed to a compromise, the deadlock would persist.