I expect it has to do with money but is much more complicated than simply allocating a small yearly amount. By way of related analogy consider housing. If you provide a subsidy but the market is primarily constrained by an inelastic supply then all you will accomplish is raising rents. I assume that there are many such nuanced factors that all contribute to the birth rate.

Hungary might also have a problem with too many young Hungarian women living abroad. It is hard to raise fertility if your locally present fertile population has already tanked.