TVG, You have a lot of variables here, so I am going to throw a bunch of stuff at you.
Answer my questions as best you can, please.
Among other things, using two different interfaces is generally a recipe for trouble.
Let's see if we can get you sorted out.
What is your OS(XP,Vista,W7,W8)?
Is the E-MU0404 USB or PCI? These are very different animals.
What driver mode are you using(ASIO,WDM,MME)?
You say the problem started when you came back to the project.
Did the computer go into sleep/hibernate in the meantime?
If XP,this is a notoriously bad routine, and rebooting the computer may cure the problem.
Also check your power management settings. If the USB port got turned off,you may have lost the Alesis(and/or possibly the 0404 if USB).
I may have more questions for you, but they will be contingent on the answers you provide, so plese be as detailed as possible.