Slate recently published a video titled "The Bubble Test," where they conducted a texting experiment between two iPhones, to see when the typing indicator bubbles might disappear.
The video revealed that after the typing indicator bubbles appear, they will stay on an iPhone user's screen for up to 60 seconds as the other person continues to type their reply, or begins to type but fails to send.
After that point, the bubbles will disappear. Even if the other person edits their response or resumes typing after the bubbles have disappeared, they won't come back.
So if you're seeing bubbles that disappear, it's simply because your conversation partner is typing a response (or lack of one) that is taking longer than one minute.