Is it possible that you have a height defined on the layer? If there is a height specified in the properties, and the CSS "overflow" property is set to "hidden", then the content of the layer is clipped, and no scrollbar is provided.
I guess either try eliminating the height if there is one set (leave the height field blank) or try adding a css rule for that layer in the CSS panel that declares "overflow: visible".
This will cause the content to spill outside of the container and be visible. Hope this helps.
-john
