I decided not to use the Ajax combobox for other reasons, but I still figured out how to add 'onBlur' attribute for the combobox. You have to add 'onBlur' attribute to the textbox control in the combobox.controls instead of adding it directly to the combobox itself.
Dim txtStartTime As TextBox
txtStartTime = cbxStartTime.FindControl("cbxStartTime_TextBox")
If txtStartTime IsNot Nothing Then
where cbxStartTime is the Ajax combobox, and txtStartTime is the inner control.
This method will fire, but the behavior does not look like 'on lost focus'. It is more like 'on selected item changed'. I guess the textbox loses its focus as soon as a user select an item from the combobox.