Bartleby will probably continue to moan through at least the end of Empyrea, and maybe until the end of the next two worlds as well. Most story arcs have five worlds, and Empyrea will be world #3 in this current arc.
Is it normal that bartleby is still wilting and moaning after his eye of history was returned? Is this happening for you guys?
Yes, it's normal. Remember that the threat from Grandfather Spider and his children is still present, this is what is causing Bartleby's illness. Restoring his eye was only part of his cure.
I guess the eye needs some time to settle down. Your cold doesn't immediately go away after taking one dose of cold medicine right?
(Also, I believe that the Eye was only suggested to help Bartelby a little bit. It's possible it wasn't actually a cure, just something to stop him from getting worse)