As mentioned previously, it's likely a folded burr, albeit very fine. It is possible for a very fine burr to fold and still not be seen by the 'reflected light' observation technique.
I don't rely on visual tests for edge quality or indication of a full apex (like the Sharpie method, which can also be unreliable), but instead focus completely on what the edge is actually doing in cutting tests. The observation that the edge 'sometimes tears paper' and 'sometimes doesn't even cut into it' is classic fine burr behavior. The variability of it's behavior is what's indicating the burr is moving & folding. It's more common in softish, sometimes cheaply-produced blades with questionable heat treat and/or heat-damaged edges. I've seen it in a few of my knives, and the fix usually comes down to grinding away the weakened steel near the edge, until the remaining steel behind it starts to exhibit more stability. To do that, I lightly draw the edge vertically over the stone (coarse/medium grit) to scrub the suspect steel away from the apex, then reset the bevels to a full apex and try again. Sometimes, that weak burr-prone steel needs to be scrubbed off a couple or three times, before the edge begins to behave with better stability.
It may still be a good blade that doesn't have heat treat or heat-damaged issues, with just a fine burr that hasn't fully been cleaned up.
My own mantra in sharpening is 'The cutting never lies'. If it's not cutting well (or at all), it can only mean either of two things: (1) it's not fully apexed or (2) there's a burr getting in the way. If it cuts paper repeatedly and easily, it absolutely proves the edge is both apexed and burr-free. That's really the only sharpness test that's proof of success.