Sorry for the delay in a reply, I have not been online (almost) due to various reasons beyond my control.
Anyway, first thing to check, that skin's wrapper.
ACP > Look / Feel > Skin Manager > (edit the skin that does not work) > Edit Header / Footer Wrapper.
Open two windows / tabs and have a quick comparison between the default skin and the broken one. Ensure that <% MEMBER BAR %> is present. Typically it will be in between <% HEADER %> and <% NAVIGATION %> , compare to another skin to see.
Hopefully that will fix it, (rebuild that skin cache afterwards and then view it on your board and press CTRL + F5)
If not...
ACP > Look / Feel > Skin Manager > (edit the skin that does not work) > All Global HTML > Member_Bar
You do not need to look at it all, the start especially is important...
CODE
<if="$this->ipsclass->member['id']">
This appears a little further down too, this is basically asking "is this a member viewing" , if this fails it will not show those links (as guests do not see them anyway)