Why are the laws of nature consistent? Is it possible for there to be an existence where (eg.) gravity works only some of the time? Why does the universe always apply the precise forces/events/occurrences in such a way that it wont let you ever catch it in a paradox?
What creates the consistency?
 A: Rather it is that science is itself concerned with reproducible, consistent results.
Dealing with inconsitent phenomena is off topic.
A: One reason is that the laws that govern the dynamics of the universe do not change with the passage of time, and neither do the fundamental constants like the mass, charge and spin of the electron for example.
A: If gravity only worked some of the time I think we'd come up with a physical law to explain when it does and doesn't work. And that law would always work. So eventually we figure out which laws do apply and when, and then we have consistent behavior. 
A: Question you ask is one of the most interesting in philosophy. It can be rephrased as: "Why mathematics is so successful in physical description of the world?" and as such was discussed many, many times, by various people from all areas of science.
As many general philosophical question it cannot be answered up to our knowledge state. Do not believe any of dudes who knows better, because nobody knows, but every generation want to give its own answer:


*

*Greeks want it to be emanation of harmony. Pitagorean tradition saying natural
numbers to be the basic building blocks for reality, which was
results of famous theorem for triangles is particularly funny example, because they discovered by itself it's not, then build a secret cult on this discovery.

*Democritus want it to be tied to its atoms properties which was
probably the deepest idea of all times drawed from pure logic. Of
course he was abandoned because of consequences.

*middle-ages want it to be emanation of God. It is very simplistic 
idea, which allows to forget about science at all.

*during enlightenment period science begin to start its growth, and answer for this question was multiplicated by various ideas. Such percolation, as we live in fact in the same period ( all we know is based on reasoning and experimentation. In culture there may be a lot of interesting changes, but science has nearly the same principles as for Euler or Lagrange) gives us a lot of various answers and of course any of them is definitive, but any of these was lectured as one and only true one.

*in our present time of high energy physics crisis, many desperated people want to explain their failure to idea that there's  no laws of physics at all, or in some variation, that there's $10^{200}$ of possible versions of reality.  It is called multiverse mania, and it is very popular in particular cultural circles. It has profound historical tradition, related to bishop Berkeley.  But mainly it's a area of psychology which explains that phenomenon, and it has nothing to do with your questions or physics.
Saying that, I would like to point you to the very first paragraph of this paper: https://www.uni-muenster.de/Physik.TP/~munsteg/arnold.html 
In my opinion Arnold is certainly right in it: mathematics is purely human activity, and reflects human point of view on reality. As part of physical science, or more generally, as activity deeply tied to real world, it is reasonable tool for reality description. Why? Hi
A: "Exceptions make the rules." The belief that nature is consistent is only a confirmation bias. 
You only see consistency because you limit the scope where you look at. When you look further, you see exceptions, you then make new rules for them, extending the consistent scope. That's also how science works, it searches and extends the consistent scope of nature.
You may then ask why this scope of nature is consistent, why the rule of gravity is consistent, or why $ 1 + 1 = 2 $. They are, because you confirm them, before you find a new exception. Even the principles of relativity, which state the consistency of nature, are just assumptions that can be and has been violated (Galilean, special, general...).
Ironically, this is a mathematical result, from Gödel's incompleteness theorems. 
