I might be missing what you want done, but I "think" a workaround would be to have the grid's refresh run a process which could call your JS scripts, then re-load the grid. This would be doing it "aware"s way. It sounds like the render script is only run once, when the grid is initially displayed.
If your grid is in a layout then this is an easy process. Have the cell be an (almost) empty html cell, with the autorefresh triggered by however its triggered now and have a process called which again, runs your JS then does a DISPLAY GridName.
Bruce