The ONLY "rational" argument for supporting capital punishment is if someone feels that certain accused killers are such a danger to society, and are so smart/capable that they could escape from any possible imprisonment, that the only way to protect society from this person is to terminate their life.
The answer to that is pretty easy, though - there are supermax prisons where the actual plausibility of escape are so remote as to be nonexistent. In cases where convicted killers have escaped, it was clearly due to inadequate precautions. There are now modern prisons where convicts remain inside their cells in solitary confinement for 23 hours per day. The doors have a multiple safety features in case of power-outages (triple deadbolts that trigger mechanically if magnetic power is lost, among other precautions), and the cells are contained in enclosed pod areas that are themselves a second layer of incarceration. These pods are isolated by passageways that again serve as another layer of incarceration. Then there are the prison walls.
The jailers never even have to physically interact with the inmates, either, further reducing any risk of hostages or attacks on workers. The inmates receive their single hour of exercise by automatic opening of their cell door that gives them access to the single hallway from their cell to an enclosed "yard" with only the one entrance/exit. They are cuffed and shackled any time their door is opened or they exit their cell. Their meals come through a rotating device in the center of their cell door.
They are allowed only their meals, their clothing, and one book at a time in their cell. They have a toothbrush and toothpaste. That's it. The lights are built directly into the ceilings, which are too high to reach even while standing on their bed. They are monitored 24 hours a day by cameras in the roof of their cells.
The prisons have a force of armed SWAT-like guards, with protective armor and non-lethal but debilitating weapons. If an inmate acts up while in their cell, they can be tasered inside their cell without even opening the door. Tear gas can be placed in their cell without opening the door. And they have no realistic way of resisting a dozen armored, armed guards if for any outlandish reason it is necessary to enter their cell and take them by force.
The prison itself is situated far from any towns or cities, and the fields around it have only low grass that can't be used to hide. The inmates have no realistic chance of even getting outside of their cells, or their pods, or the secure entries to the pods, or the prison walls. But if by some miracle -- through supernatural intervention -- the managed to get beyond the prison walls, the vehicles and armed SWAT guards and dogs would catch them in the flat, barren miles of land surrounding the prison. Escape is not an option -- this is the real world, and supervillains don't exist. Even elaborate prison escapes are easy to understand as possible due to limitations of the prison itself, and it is precisely because dangerous inmates are not properly housed that escapes by such people are ever possible.
The existence of perhaps three of the modern max prisons described above would be more than enough to house the types of criminals whose very existence poses a risk to society. Their construction allows for minimal upkeep and labor costs. It allows keeping these people alive to study and evaluate them, to learn from them so that we can better intercept and identify other people like them -- and to potentially find a way to treat and cure whatever potential mental illness or psychopathic/sociopathic tendencies drive them.
The latter point alone is important, and applies to perpetrators of sex crimes as well -- I hate rapists and pedophiles worse than I hate killers, actually. But I realize that society will be served if we can "treat" them because it allows us insight into the causes, the warning signs, the methods, etc of whatever sickness has taken over their minds. The ability to treat them, and maybe some day cure them, is VERY important to society -- there was a point in time when they had this mental sickness and these urges prior to their first acting on those urges. If a treatment or cure exists, identifying such people early and removing the threat as much as possible, and being able to treat and potentially cure them so they don't act on the urges or don't act AGAIN on those urges, will save more people.
We may prefer to mistreat the convicted sex offenders and not care to treat them -- but we either actually want to do what's best for society and what protects the most children and other victims, or we're just blowing smoke. You don't have to like or even honestly care much about the sex offenders themselves -- just care about the possibility of reducing or eliminating the threat to society overall, not just in those people caught but in the larger number who AREN'T caught, and the people in the future who would otherwise commit the same types of crimes but who can be stopped before they destroy lives.
We can talk all day about executing sex offenders, but we know it isn't going to happen. And while I believe that anyone convicted of rape or child molestation or similar crimes should be sentenced to life in prison without parole, I also know that it's not very likely to happen, either. These people get short sentences and are released back into society -- that's the fact of life, period. At best, they may some day be locked up for much longer, that's it. So the question is what can we do that is most beneficial to society, within the existing reality of the situation? The best thing is to use those inmates to learn all we can, and to try to find treatments and some day maybe a cure. So creating a prison that isolates them, removes the danger of escape, and then seeks to gain as much information as we can from them is the best option.
I think these are very obvious things, and it doesn't even require the added consideration of innocent people being wrongly convicted or other moral questions about proper treatment of convicts. Just purely from the perspective of societal preservation and protection, I think the evidence against executions and in favor of incarceration to learn and develop treatments and databases etc is overwhelming.
As for convicts supposedly losing their right/expectation of not being abused and tortured etc -- we have a Constitution. And in it, there is a specific and explicit protection against cruel and unusual punishment. It only applies to people under arrest or incarcerated, that's exactly WHO it was written to cover. It doesn't make any distinctions between severity of crimes or amount of evidence etc -- it exists solely to protect suspected and convicted criminals from punishment that is cruel or unusual, period.
To claim these people have "lost their rights" is glaringly contrary to the actual law and the actual principles on which our nation was founded. To get to a point of the accused "losing their rights" to an extent that allows intentional abuse and torture etc, would require amending the founding document of our nation and altering the perception of the application of justice. Killing, beating, torturing, etc of inmates has to fall under the definition of "cruel and unusual", or NOTHING does and the protection becomes meaningless.
Those who so willingly declare we should cast aside one of the protections of the Bill of Rights need to ask if they would so easily denounce and ignore and call for violation of other protections as well. What about speech? What about gun rights? Pick your favorite protection in the Bill of Rights from our Constitution, and consider how strenuously you'd argue why it cannot be violated and why it's important. Then ask why you would think that the protections you care about personally are more important than the other protections guaranteed by the same document, under the same democratic principles of a fair and just society that seeks to limit government intrusion and exertion of power over its citizens.