When a massive star cannot produce sufficient energy to counter it's weight the result is often a neutron star which is stabilized by quantum mechanical effects, say given enough mass to overcome such effects it becomes a black hole. I wonder if it can lose energy until it reverts into neutron star? If not why not?
I wonder if it can lose energy until it reverts into neutron star? If not why not?
Not at the moment, because nothing leaves the black hole. To lose energy/mass something has to leave, radiation or particles, and nothing can leave except Hawking radiation from the horizon, draining energy from the black hole. This is too weak to enter the picture, unless one is talking of the end of time of the universe, then yes it could happen
A scenario with two black holes falling into each other and losing energy in gravitational waves (LIGO experiment) , would still create a new black hole where nothing substantial leaves. I do not know whether a limiting condition, where gravitational radiation is large enough but the joint mass not enough to form the new black hole, might exist. I suspect not.
No it can't.
Anna is right that mostly a BH can't loose energy or equivalently mass. But it can for some conditions as Anna wrote, like the Hawking radiation and when two BHs merge, the combined mass will be less than the sum of the two because they loose energy to gravitational radiation.
But in both those cases the BHs sizes change correspondingly so they remain BHs. For the Hawking radiation the mass is reduced, but the BH then gets smaller and it remains a BH. Until the end where it is so small and evaporates so quickly that it explodes by releasing the Hawking radiation very rapidly. Then it ceases to exist. The rates of decay are well known, a function of size/mass, and as they get smaller they decay faster. Large BHs like the one at the center of our Milky Way can last for 100's of billions or trillions of years.
For the merged BHs, the resulting merged BH gets more massive, but also bigger. Since the mass of a BH is proportional to the horizon area (and so to the radius squared), which is proportional to the entropy, and the total entropy has to increase, the the mass and entropy increase for say two equal BHs combining, but the radius increases at most as the square root of what the mass and entropy increases, so it always remains a BH, as merged. In fact this type of calculation (I simplified, but it's true for all cases that it always remains a BH plus whatever gravitational radiation it releases) was used to figure out the maximum gravitational radiation that can be released, as the total entropy can not decrease [for instance if no BH remains and it all goes out as gravitational radiation or something else, the entropy would go down - per unit area a BH has the maximum entropy possible]. See Binary BHs and mergers at e.g., https://en.m.wikipedia.org/wiki/Binary_black_hole
The percent of the total BH mass/energy released in gravitational waves for the first LIGO detection was about 5%. Limits possible have been calculated as I described above, and they vary depending on kinematic parameters, spins and charge if any, but they can range from about 27% to more than 50% (and I don't remember the exact numbers for the max).
As for a neutron star forming in that latter case, the radius (of the possible horizon) remaining will always be less than the (eg, for spherical symmetric, but also for the Kerr type) Schwarzschild radius, and so will already be a BH.
So no, nothing other than BHs or nothing an remains behind.