Definitely try and ask for advice, send a friendly email to your POI and see if they can give you a few pointers. For example, they may have read your SOP, but thought your research interests were not concentrated enough or did not fit with them to the extent they would have liked. Or maybe, they didn't even see your application because it was eliminated during a screening process due to GRE/GPA. This is important information to know and will help you tremendously during your second cycle. Also, SO MANY people have bad luck their first application cycle, you're not alone, and it doesn't mean that your not "graduate material", so don't give up!
To answer the second part of your post, if you would be going into a significant amount of debt to get your Master's, I wouldn't do it, however, if the program is able to fund you by means of a graduate assistantship or scholarship and you are interested in the school and the program, I would say go for it. Especially because you think that your lower than average GPA may be one of the things keeping you out. Aim for a 3.8+ in the Master's program, and that will help your GPA a lot!
The GRE, however, is a beast of its own and will require additional studying whether you get your Master's or take a year off. I have heard that it is A LOT easier to study for the GRE when you take a year off, so that could also be a consideration for you. Retaking the GRE is not something that a lot of people are keen on doing, but if you are willing and think it will help you get into a program go for it. Just a side note....My SO got accepted into his top choice program (which is extremely quant. heavy) with a GRE quantitative percentile of 38. He never got questioned about it once during any of his interviews and it also didn't bar the admissions committee from admitting him after his POI recommended him. In the end, how important is the GRE score? I can't really give you a solid answer, but I don't think it's as important as some make it out to be.