Let me add to P_Bartell's sound advice. Not only is nothing sacred about p=0.05, I would advise against any threshold value without doing some kind of decision analysis. If you use a threshold (and realize that perhaps none is necessary - usually, I'd advise to build the model and report the results, regardless of p values) to make binary decisions (such as keep the variable in your model or not), realize that either way there is some possibility of error involved. You should think about the relative costs of errors before deciding what cutoff to use.
Beyond that, cutoffs are generally a bad idea. I don't advise dropping "insignificant" variables from regression models - ever. The variables presumably were there for a reason. You thought they should matter. If the data is insufficient to reveal their influence, then so be it. Dropping the variable amounts to deciding the variable has no influence, something you don't have evidence for. Further, all the other variables in your model will then have their coefficients changed - are you prepared to say these will now be more accurate than they were before?
Despite the widespread use of p=.05, you should check the ASA controversy over p values and some of their recent statements about this. Some psych journals have gone so far as to banish p values. Many journals will still reject papers that don't have p values < 0.05. In the midst of such confusion, here is my own opinion. I want to know the p value - I believe it is an indication of how strong the signal is regarding that variable, in the data I have (note that even that statement is open to considerable criticism). I prefer not to see any binary choices made: I try to never say variable X does or does not influence outcome Y. It is always a matter of uncertainty and strength of evidence. The p value is part of that evidence, and when it is high it is telling you something. Omitting a variable due to its p value is deciding something that is not evidence-based (it is tantamount to saying that variable X does not matter). If you have few observations relative to the number of potential factors, then you can use Predictor Screening to assist with choosing which ones to use, but there is nothing you can do that will change the fact that your data may not be sufficient for the models you would like to build.