Compared to secondary research, primary data may be very expensive in preparing and carrying out the research. Costs can be incurred in producing the paper for questionnaires or the equipment for an experiment of some sort.
In order to be done properly, primary data collection requires the development and execution of a research plan. It takes longer to undertake primary research than to acquire secondary data.
Some research projects, while potentially offering information that could prove quite valuable, may not be within the reach of a researcher.
By the time the research is complete it may be out of date.
Low response rate has to be expected.