Faith is trust in Christ as the propitiation of our sins plus outward confession of Him as Lord of our life, i.e., the master of we who are His slaves, meaning we must obey Him, being part of His program. If we don't get that part right, all the trying to get close to God in the vine is for naught.
So, can you lose your salvation? Can we be unborn again, de-regenerated, Spirit-undwelt, having your name blotted out of the Lamb's book of life, etc?
Sure. Stop believing in your heart, and stop confessing him with your words and actions. Then, as you both seem to point out, your faith is dead. End of story. But, I contend that true believers never stop doing those things. Does that mean a true believer won't fall? NO. But a true believer, like Peter after disowning Christ, repents, and seeks reconciliation with the Lord in forgiveness. Problem is, many who think they are true believers may be wrong.