Why is the polyurethane finish I applied a month ago still tacky?
Depending on the type of Polyurethane, they could cure first by solvent flash off, then by oxygen or water in the air, or by some other curing agents in the mix. What product did you use?

Sometimes very thick layers of Poly will not cure because the layers below the surface cannot interact with the air or the surface blocks the solvent evaporation of the lower layers. This interaction causes the whole thing to stay "tacky" for a long time.