It's difficult to advise without better explanation of how you are creating the grids and using them to constuct the artwork, the size & number of grids invloved, and the kind of artwork you are building. But on the face of it, it sounds like a poor workflow.
So far, it almost sounds like you are drawing grids and filling them with color so as to make a mosaic that would be the vector equivilant to a raster image--a pointless excercise.
Explain exactly and completely what you are doing, which tools you are using.
I made this a 24 x 36 inch document with each inch divided by 8.
Then made it live paint Group and use d the bucket to fill in areas by dragging over the areas rather than one square at a time.
If you get rid of the strokes first before converting t a Live Paint group you have no spaces between the squares.
IF you want you can draw a rectangle to the size you need then Go to Object >Path>Split into Grid and leave no space for the gutters then you have a grid as well that can be filled individually or as part of a Live Paint Group.
You can also go to Object> Expand and object flatten Transparency and that might help as well.
The other thing you can do is every so often save the fie and quit and relaunch Illustrator.