If you have a database of 50 studies with outcomes for all, but the data for each moderator is not available for all of them, can you perform a meta-regression?
I believe you would be limited to only those studies reporting the moderator(s). How many of your studies contain these data? You could run the meta-regression on that subset of data for your analysis. But it may also be fruitful to test for funnel plot asymmetry in the full and reduced dataset to ask if there is some bias in the subset of data reporting the moderator of interest.
Yes, I agree with Mr.Becker. It is reasonable to limit those with available data for your meta-regression finally. Of course, it should be necessary to explain your selective criteria for those studies in your meta-regression. Theoretically, the heterogeneity and bias of this subgroup of those with available data are best not to influence the interpretation of the overall results.
I think it is totally fair enough to use the subset of studies as long as this is clear in the resulting paper. Asking the authors for more data is always worthwhile. It would be unorthodox, but actually statistically conservative to substitute a median value - note i have never done this, but if you are more afraid of a type I error than type II it is reasonable.