I'm facing separation due to failing my 2nd record APFT within a year. Can I take terminal leave or DO I have to sell them?

Leave is always a request, and while it is normally approved.. nobody here can say for sure,, that is a question for your chain of command>
From the other side of the street..... you are still on the books for the unit even on terminal leave.. yes different category but still there.. Known loss, and all that... For reasons only you and the command know, you are being involuntarily separated … While you have stated the separation being used,,,, I would have to assume there is more to it… and that more will likely impact the approval of your leave request. If there is no “other side” of the story, I’d think your leave request will be approved.. but again, only your commander knows
Good luck, now go ask.

The best place to get an answer to that question is your local I.G. He/She will have ready access to all applicable regulations and can properly advise you on applicability and how to apply. They will also be subject matter experts on military separation, regardless of reason, if you wish to appeal an involuntary discharge. The final authority for any decision concerning that action rests at the Two-star level of your command. You have the right to appeal such separation action if you have not already done so. Not every "body" fits the nice, neat, parameters of the military's physical fitness program. There are exceptions to every rule. That Two-star has the authority to overrule separation "IF" the service member displays an acceptable military appearance, demonstrates satisfactory job performance, and desires to continue their service. I do not have the facts of your particular issue before me, so can't comment further, but if any doubt exists in your mind and you wish to stay in the military, then I strongly recommend you seek assistance from your local I.G. If you still face separation, at least your mind will be settled that you have utilized all applicable avenues available to you for resolution.

It is financial beneficial to use your terminal leave as you receive BAH, COLA (if applicable), medical benefits and so on versus cashing in and paying taxes. In the end it is your decision. As many have mentioned, it has to go through the approval process. Be the subject matter expert of your own transition so no one give you BS. Good Luck.