Bathroom faucet drip
There should have been a 'packing' in the stem assembly.  This is usually a gasket or a series of gaskets that prevent water from seeping around the stem when the stem is in the off position.  If the packing was in good shape (no cracks or brittleness) and was seated properly then I would say it's time to replace the whole fixture. 

In my past experience if the leak doesn't come from the stem or the packing around it, then the time finding the problem and the cost to fix it usually is not worth it for a cheaper fixture.