The following steps create this issue:
1. Use html 4
2. Use telerik AJAX (For consistency)
3. Set a radgrid with some columns that reach beyond the extent of its element (such that it requires horizontal scrolling). Use at least four columns. One being the GridClientSelectColumn.
4. Have the following settings:
Control Settings: 
AllowPaging=true,AllowSorting=true,AllowFiltering=true,AllowFilteringByColumn=true,AllowMultiRowSelection=true

Control Events Used: NeedDataSource,OnItemDataBound
Client Settings:
EnablePostBackOnRowClick=false,Resizing AllowColumnResize=true, Selecting AllowRowSelect=true,UseClientSelectColumnOnly=false,Scrolling,AutoGenerateColumns=false,AllowScroll=true,UseStaticHeaders=true

Important note: Retain data on the server, rebind, and, on item databound, select the previously selected rows.

Set up a button to perform some action on the selected rows and have this action use AJAX such that this action depends on the currently selected rows in the RadGrid.

5. Scroll away from the selection checkboxes
6. Select some rows in your RadGrid
7. Perform your action with AJAX
If all was set up correctly, your grid should have been rebound with the previously selected rows re-selected. The RadGrid should still be scrolled to its previous position.
8. Perform your action with AJAX again. Here's the bug, the grid states that it has no selected items; however, the client shows that there are items selected in the UI.

This may be related to "RadGrid's last selected item index is not persisted correctly when two or more postbacks are triggered from external controls."