The popular view of science is that it is firmly rooted in empiricism.
A statement is true if it can be empirically verified, or if it is a falsifiable statement that hasn't yet been falsified, and scientific fact is made up of these many individual statements.
This is a large over-simplification.
Before such observations can be made, a framework needs to be in place.
To design a good experiment, the possible variables and constants must be considered before you know what to observe. When you make an observation, it's very important that you know what you are looking for.
Another important thing is that concepts must be defined.
Our scientific concepts aren't always physical objects that we can simply point to and name.
Concepts like 'force' and 'energy' are defined by the mathematical equations, the role that they play in the theory as a whole.
Such a theory must already be in place before we can start observation.
We call such grounding theories paradigms.

Introducing the paradigm
The paradigm is the background theory on which individual statements rely on for structure. Perhaps the best way to understand the paradigm is to show the examples in history.
(The concept of a paradigm actually arose from Khun's study of the history of science.)

The cycle starts with a paradigm in place.
As the paradigm isn't perfect, problems gradually pop up and start to put a strain on the coherence of the overall theory. Eventually so many problems arise that the theory is becoming more or less incoherent, it is said to be in a crisis.
A new theorie arises, one that provides for the problems faced by the old theory.
This new theory kicks off with new promise and the old is gradually discarded in favour of it and it becomes the the dominant paradigm, and the cycle starts again.
The first paradigm of physics came from Aristotle and became the dominant medieval scientific worldview. It gradually got replaced by Newton's theory of motion. This wasn't down to a single observation or logical argument.
The more that scientists explored, the more problems that Aristotelien paradigm faced.
Over a couple of hundred years, slowly develloping from original ideas from Copernicus through devellopments with Galileo into a fully extensive theory from Newton, a new theory arose that seemed fit the observations of the day much beter. The Aristotelien paradigm fell into disuse and Newton's theory of motion became the dominant background to research in physics.

In turn, the Newton's own paradigms develloped problems and had to be replaced by Einstein's general relativity. Once again, it wasn't one or two observations that falsified the theory. Problems built up over a hundred years, culminating to the point where Newtonian physics was losing coherence in it's attempts to explain the data.

Are paradigms beyond criticism?
So what relevance has this to the question of whether theism is rational?
Metaphysical positions are also of a paradigmatic nature.
There are not proved or disproved by individual observations or arguments, rather they are judged by the number of problems they face and how they explain existence as a whole. This gives the following possibility:
If a theist doesn't accept a seemingly flawless scientific argument, this doesn't necessarily mean that they reject reasoning, it's just that the reasoning in this scientific argument depends on the paradigm that it is based on. If they are working in a different paradigm then their own rational investigations will give them different results.

Some take this too far and declare a relativism on paradigms.
There is no 'right' or 'wrong', just everyone works with their own assumptions.
Just because there isn't a clear cut method for judging paradigms, this doesn't mean that they are beyond judgement - it just means you can't make instant snap judgements with individual arguments and observations. Instead we must look at the over-all performance of the paradigm.
Our paradigm devellopment is evolutionary. In physics, a paradigm that is facing too many problems is replaced by one that can deal with these problems. This is similar to how we devellop our own worldviews. At any time we will be holding a number of background assumptions that cannot be directly justified or falsified, but as our experience grows we find that some are vindicated in giving us a clear picture of the world while others we find we have to drop.
It is a gradual process of fine-tuning, an infinite amount of subtle steps, slowly culminating in a clearer insight on the world.

It is possible that the reason why the theist believes is because their current stage in worldview brings them to a theistic conclusion. It is also possible that they are using 'paradigm difference' as an excuse to ignore reason and close their mind off to conclusions that they don't like. Once again, it's not the content of their belief that determines whether they are rational or irrational, it's their attitude to this belief. Are their paradigmatic assumptions open to change in light of new experience or are they rigidly holding to a dogma?
It seems that the only way to judge whether they are being rational or not is to see how they behave in debate. See their attitude to reason. It's quite possible that a rational person could come to quite absurd conclusions on their journey - it's the nature of trully testing out the possibilities. On the other hand, if a person is stuck in the same paradigm for 30 years, oblivious to the problems it faces and not moving on, perhaps that's a sign that they've closed their mind to reason and sunk into dogma.
The key point is that it's not the content of the belief by which we can determine someone's rationality (i.e. by whether they are theist or atheist) it's their attitude to reason and debate that is revealing.