It may be due to some other style overriding the padding of your css. Inline styles takes preference and so they are applying.

What you can do is - apply the css to your element by its id. For example if you give your 'td' id as 'myEle' then you can do this:

<td id="myEle" colspan="2" class="TableEnrollHeader" style="padding-bottom:0px"><asp:Label ID="Lb_ActivityName" runat="server"/></td>

#myEle{
    background-color:#ba9c78;
    font-size:larger;
    color:white;
    height:30px;
    padding-left:10px;
    padding-bottom:0px;
}