Your problem's cause is rooted in a a basic economic principle, supply and demand. When you quickly reply to each email, you become a cheap resource for help, undermining the usefulness of the client thinking through problems themselves, or perhaps thinking through their problems a bit longer before sending another email.
The solution? Delay your responses by 1-2 hours. Decreasing the supply on your side will serve to increase the "cost" of each interaction, since they have to wait for reply. You'll find the emails stop sounding as frantic and disorganized/incomplete, and not as many are sent.
Great point - I didn't even think of this. To add, I would reply to them once or twice a day, in one condensed email that addresses all of their emails.
Also - I use Gmail for my business account so I can easily click on the 'Move To.." -> "Label" button, effectively archiving and organizing it at the same time.
The solution? Delay your responses by 1-2 hours. Decreasing the supply on your side will serve to increase the "cost" of each interaction, since they have to wait for reply. You'll find the emails stop sounding as frantic and disorganized/incomplete, and not as many are sent.