If you received a field grade article 15 and your appeal got denied over non direct circumstantial evidence, how can you still fight?

You can always request trial by court martial. However, since I have never heard of this particular worded situation, my recommendation is that you seek out JAG for the best legal counsel possible.

An Article 15 is non judicial. If you wanted a judicial proceeding, then you should have chosen a court martial. Non judicial punishment gives Commanders wide latitude to use their judgment in cases and doesn't adhere to rules of evidence as strictly as a court martial.

Your options are pretty limited. You could try and convince the Commander that imposed the punishment to set aside or suspend part or all of the punishment. Since this is a field grade Article 15 unless it was imposed by one of the few company level Commands that have a MAJ for a Commander you will need to get the CSM in your corner if you have any hope for success. If it is a MAJ Commanding a Company then you will need to get the 1SG's endorsement.
The only administrative relief that I can think of would be to request the action be removed from your records.
The Commander that imposed the Article 15 can do this but the standard for to do so is pretty high. There would need to be exculpatory evidence.
You could also apply to the DA Suitability Evaluation Board to move the record from your performance fiche. Generally, the won't act until sufficient time has passed to show the punishment served the purpose.
Finally, you petition the Army Board for Correction of Military Records. Similar to asking the Commander, you will need to show an injustice occurred.
At this point, you cannot request trail by Court Martial.