The data determine what is estimable. Omitting one of the runs will limit the model that can be fit. It is OK, though. Remove the term that would cause the singularity. For example, if you omit either the (-1,-1) or the (+1,+1) run, then you must remove the interaction term from the model or else it will cause a singularity in the linear regression. So the nature of each run is important in defining which effect is estimable.

Remember that with only three runs, it is possible to estimate the intercept and the two main effects. It is impossible to perform any hypothesis tests on the model as a whole or on individual terms. So the number of runs is important in defining which tests are possible.

Learn it once, use it forever!