I don't have Maya open so this may not be totally accurate.
I think the problem is that Maya is solving these in the wrong order. Right click on your character, the choose "All input Connections" or something similar. Here you will have a list of all the things inputting to your mesh, the smooth skin's cluster, the blend shapes, anything else you may have made in terms of deformers.
What you need to do is have (I think) the blend shapes as low down the list as possible, certainly below the smooth skin cluster. If not, try above. Once it's in the right place though it should solve your problem instantly.