The amount of data needed will depend on the usage you plan to give to the results of the data-mining. Depending on the case you could want to show how the answers are distributed or maybe try to find some relations between answers. If the idea is to obtain some relation between answers to detect different interesets for example I reccoment obtaining as much questionnaires filled as possible, and from diverse type of people to avoid biasing. As bigger is the number of filled questionnaries you obtain, more confident will you be about the findings you are able to make.
In theory, the more data sets, the better, but there are many ways to use when there are not many samples, including re-sampling. When you use data mining tools, power verification is a good tool to help understand the persuasiveness of sample numbers for data exploration results. Moreover, you can read the relevant literature to observe the sample size, and then try to collect the number of samples close to the number. If the result is not good, it may be a statistical problem such as the category deviation when collecting the sample. Further analysis and recollection of the sample are necessary.