Will I still be eligible for TA next semester after failing class while using TA?

Wait, you missed the exam because of a field exercise? There is a process that exists for situations like this, were the Soldier does not have to repay TA out-of-pocket. See this memo: https://www.goarmyed.com/docs/wm_memo.pdf

Also, see Paragraph 4a (last sentence) and 4b of the TA Statement of Understanding, provided below:
https://www.goarmyed.com/docs/Annual_TA_SOU.pdf

While I can't answer your original question, I don't want to see Soldiers having to repay up to $750, if they are being caused to fail courses due to no fault of their own.

I'm not going to speculate on whether your Commander had knowledge of your exam, prior to having you participate in the field exercise; or whether you were negligent in informing your Commander about the exam. If the information is relevant to your situation, ask the questions, and use the regulations to your advantage.

Ask your base education office. They will be the SMEs

I had a similar situation and failed a class because of it. As long as you create your repayment plan on goarmyed, they will continue to fund your classes. I am still paying a class off and TA is funding my current classes right now!