To state my conclusion baldly, I think these people are involuntarily shifting themselves between "third density" and "fourth density", something the "aliens" seem to do at will.
To accept this shifting, one must first accept that there are such things as third and fourth densities. This is a major "if." Acceptance of different densities is not easy. It is a concept that belies what our senses tell us, and seems to lie well outside the realm of human scientific knowledge. I won't pretend to understand the density concept, but in my mind I had assigned it a fifty percent probability, essentially true or false. The report of involuntary invisibility seemed to connect to what little I understood of the density concept, and if it were true (again a fifty percent probability) it tended to confirm the density concept. That is what I meant by "fit." There is no "proof" here; just a shift in probabilities.
In addition to acceptance of density reality, it is necessary to accept that: 1) the "aliens" exist, 2) that they are abducting humans, and 3) that they are making changes to abductees which include the ability to shift density at will. In my mind, I have assigned the first two a high probability of truth, and the third a probability higher than fifty percent, based on the "fit" mentioned above. Provision of the shifting ability makes sense if abductees are being prepared to carry out some task germane to "alien" plans, as indicated in much of the abductee literature. If such a tool is being provided, the people who are experiencing involuntary switches in density may be having difficulty digesting the "alien" tampering, a not uncommon phenomenon. The shifts could be a sort of psychic hiccup.
If all of this is true, it would behoove the persons who are experiencing the problem to be very careful not to let the military know it is happening to them. It could be fatal. I can think of nothing that would terrorize the paranoid minds in the military intelligence community more than the ability of someone to become invisible. Come to think of it, your banker wouldn't be very happy about it either.
In displaying this hypothesis, I make no claim to "truth". This is just my "take" of something that I can only experience at second, third or fourth hand. I have been asked for my thoughts, and have expressed them as they are at the moment. The picture is constantly changing, and more puzzle pieces keep appearing. Probabilities shift and relationships are altered. I don't really expect to see a "final solution", but it is endlessly fascinating to try to solve.