Firstly we must establish that justice is indeed mutable when concerning law within a democratic political system before we discuss measures of righteousness or solutions for dealing with a lack of such.
The majority of western justice systems include measures to amend the law through either the courts or government (in some cases, both). In fact, nearly every democratic country has measures for law addition or amendment by the government. Whilst democracy itself is purely a system of government rather than a statute for how justice is to be determined or whether it be by the elected government, the political theory behind democracy clearly includes the principle that all citizens are equal before the law. Whilst not implicitly stated, it is implied within the very values of democracy that a democratic government should have the power to amend the justice system to better reflect the principle of all citizens being equal before the law.
So, we assume for the remainder of this argument that the justice system is intimately entangled with the principle of a democratic governance system, and therefore measures of a democracy's "righteousness" can theoretically be performed on the quality of the justice system. This measure, as laid out in the description for this debate, should be discretely measurable.
What is far harder to assert within the context of this debate is whether a measure of the righteousness of a democracy in regards to its justice system is even possible, and if so, whether this should affect the ability to amend the law. Scientific measurability is extremely difficult to perform on something that is firmly routed in concept rather than physicality. How exactly does one measure righteousness, and how does one apply that inexact measurement to something as complex as an entire nation's justice system?
Measures of the ability of a justice system are usually performed on conviction rates, or some other measure of effectiveness of conviction or reduction of criminality. However, the current amount of offenders currently being processed (either in prison or awaiting a trial, etc) within the justice system is simply a measure of the effectiveness of the implementation of the laws in place and the effectiveness of enforcing those laws. This is evidently no measure of how right (morally or otherwise) those laws are, or how right the enforcement of those laws are. How do we even begin to discretely quantify a measure of righteousness, and even if we jump that hurdle, how do we apply it to laws? The simple answer, and the one posited at the beginning of this debate, is that we are unable to effectively measure (in any scientific manner, at least) how righteous a law or the enforcement of said law is.
However, I disagree entirely with the solution suggested. I would even go so far as to say that a lack of any scientific measure of the righteousness of justice would in fact point to a solution that specifies that justice must be mutable.
If we ever found an effective measure of righteousness, then justice would be eternal. We would create our laws, create measures to enforce those laws, set up a fair justice system and then effectively end any discussion of what is and isn't fair and just. This assumes an absolute morality though. This would be the only situation where we could have an immutable justice system, because there would never be a need to modify it.
Morals and society change. What would be classed as both morally and legally acceptable even a hundred years ago may now be deemed wrong and illegal. Is this because society was moulded by changes in justice, or was justice moulded by changes in society? (This is most likely a subject best kept to another debate, as it is extremely wide ranging). I suggest that society is always at the forefront when it comes to either justice or morality.
The morals of society drive and mould justice, and this is heavily reflected in the way that the current democratic systems work. Actual governing is carried out by the people governed or the power to do so is granted by them. Members of society choose to elect leaders who, in turn, reflect the wishes of the people within the law. Society picks it government, and its government amends the laws based on the will of the people. (Again, this is something that can be left to another debate: is democracy really the will of the people, or a charade of such?).
If we stick purely to the theoretical aspects of democratic government, it should hold that justice is entirely mutable, and, in fact, a mutable justice system (one with an effective measurement of its righteousness other than by reflecting the wishes of the people) is one of the indicators of a democratic government.