WebGrid will rewrite the style and class name after updating a row. If you wish to preserve the style you set during ExitEditMode client side event you will need to buffer the modified style during BeforeUpdate client side event handler and re-apply the style during AfterUpdate client side event handler. Here is the snippet, I am using class name to modify the edited cell:

var EditedCell = "";
var KeyValue = "";

function wgTest_OnExitEditMode(controlId, tblName, editObject)
{
	var wgTest = ISGetObject(controlId);

	editObject.cellElement.className += " Edited-Cell";
	
	return true;
}

function wgTest_OnBeforeUpdate(controlId, tblName, rowObject)
{
	var wgTest = ISGetObject(controlId);
    
	var rowStruct = ["ID", "Name", "Author", "Category"];
	for (var i = 0; i < rowStruct.length; i++)
	{
	    var className = rowObject.GetCell(rowStruct[i]).CellElement.className;
	    if (className.indexOf("Edited-Cell") > 0)
	    {
	        EditedCell += rowStruct[i] + ";";
	    }
	}

	KeyValue = rowObject.KeyValue;
	EditedCell = EditedCell.length > 0 ? EditedCell.substr(0, EditedCell.length - 1) : EditedCell;
	
	return true;
}

function wgTest_OnAfterUpdate(controlId, tblName, rowObject, xmlResponseObject)
{
	var wgTest = ISGetObject(controlId);

	setTimeout(function()
	{
	    var rowEditObj = wgTest.RootTable.GetRowByKeyValue(KeyValue);
	    var rowStruct = EditedCell.split(";");
	    for (var i = 0; i < rowStruct.length; i++)
	    {
	        rowEditObj.GetCell(rowStruct[i]).CellElement.className += " Edited-Cell";
	    }
	    EditedCell = "";
	    KeyValue = "";
	}, 10);
	
	return true;
}

This solution is not working for Firefox and Safari.

In my test for both FireFox 3.6.3 and Safari 4.0.5 I found that the method will work without any issue. The edited cell will have a red color as the result of the snippet.