This is an interesting problem to resolve. The problem is the some browsers (including IE) do not allow to set and innerHTML for the <select> tag.
The best solution is to redraw the entire <select> tag. It works!
Wrap the <select> in a <td> or <div> with an id.
As per my opinion, the innerHTML which you're trying to set looks like a collection of <option> tags, like - "<option>...</option><option>...</option>".
Instead of this, it should be like - "<select onchange=\"some_function()\"<option>...</option><option>...</option></select>"
...and this should be set as the innerHTML of the wrapper <td> or <div>, as:
Hope this helps!