In addition to Rami's questions, a general answer is that sample size is weakly related to the nature of the model you are going to use. The sample size issue is more about the test you are are using to assess whether you can reject H0 for one or more model coefficients. For instance, for linear models, z tests for coefficients are asymptotic, i.e. hold only for large sample size (say n / k >> 10 as a rule of thumb, with n the sample size and k the number of model coefficients). When these conditions are not met, you can still use the linear-model methods to estimate the coefficients, but it is wiser to use bootstrap methods for the tests on model coefficients.
It could be that in your situation regression analysis is not suitable. It is impossible to provide a useful recommendation without knowing more about the experiment and about the data.