Karl Popper taught us the importance of looking for refutations. Any view worth believing in, MAKES PREDICTIONS, and can be refuted. His early thinking about this process needed revision, as it treated refutations as individually decisive. However, because theory is underdetermined by evidence, EVERY theory can be patched to address any evidence. Therefore, one needs an additional criteria to evaluate when accumulating patches make a theory effectively refuted.
Popper's solution was to reformulate Occam's Razor in terms of predictive power. When modifications to patch a theory produce no predictive power, they are pure desperation patching. If the major tests of a theory all call for pure patches -- it is probably time to toss it. This is, of course, a subjective judgement, which all Occam tests are. But it is at least less of a pure judgement than "simplicity" is.
Lakatos came up with a better version of Popper's falsificationism, with his progressive vs. regressive research programme: http://people.loyno.edu/~folse/Lakatos.html Lakatos approach seems to describe well, how science ought to be done. It too, calls for judgement.
The other recent idea which has a bearing is consilience, which is explained here: http://warincontext.org/2014/01/28/the-importance-of-consilience-in-science/
Discussions between theists and atheists often feature a lot of ad hoc patches. Both parties generally are unmoved by their patches being pointed out, because they each think there is a consilience of evidences supporting their research programme, and it offers enough value in living life that it is progressive despite the occasional need for ad hoc patches. They both also generally presume that they can find better patches soon that will be less ad hoc, so even temporary apparent regressivity is just a "bad patch".
It is very difficult for someone to do an honest evaluation of a worldview they hold by. One can try to total up the negatives and positives, and try to figure out if it is progresssive or regressive, but the answer will almost always be "progressive" by using weighting of different issues differently. But -- for someone experiencing a set of negative evidences -- there often is an unconscious realization that one's worldview is under justifiable threat. Those who abandon/deconvert from a worldview, generally do so because an accumulation of issues just became to stressful to them. This is -- a consilience of evidences forcing the realization that the programme is regressive!
I hope this answer is helpful.