I feel that there are at least two things to consider here.
1) Whether used in statements or questions, 「だいじょうぶ」 has so many different meanings and usages.
2) You might be missing the non-verbal ways of communication employed by your teacher.
Seriously, 「だいじょうぶ」 is like a king of expressions in informal daily speech. It can mean:
"O.K.", "all right", "will do", "satisfy", "convenient for one", "not injured", "enough", "safe", "fine", "right", etc.
I could keep going if I were willing to ruin my autumnal 3-day weekend. You stated in your comment above:
When I asked my teacher some questions, she will reply to them but follow up with 大丈夫ですか。Or when my teacher taught my class something new, she will also ask us 大丈夫ですか。
This 「大丈夫ですか。」 would mean something along the lines of "Do you understand my explanation?", "Are you following me?", etc. as @Chocolate stated above.
You could reply, 「（はい、）だいじょうぶです。」 or just 「はい。」 to that question from the teacher if she were speaking specifically to you.
If, however, she were speaking to the entire class, not everyone would need to verbally reply. You can choose to just nod or just let your eyes "say" 「だいじょうぶ」.
Would the teacher reply, in return, to that verbal reply by a student? She might not verbally do so, but she might non-verbally by nodding and/or eye contact. Japanese-learners miss this all the time. They tend to expect actual words to be uttered, so they feel like their teacher is not acknowledging their 「はい、だいじょうぶです。」.
It would take some time,but you will eventually learn to communicate non-verbally with Japanese-speakers.