I don't believe this will be possible in LV 7.1, but in 8.0 and above it certainly is. (It's possible I'm missing something, so if someone wants to correct me, feel free

). Here's the reason:
The problem you seem to be having is that the popup VI you are using to display the graph data is non-reentrant. What that means is that there's really only one copy of it in memory, and everything that calls that subVI has to share that one copy. Only one call to it can be made at a time. This is why you only can only pop up a graph on one signal at a time.
There's also a notion of reentrant VIs. Reentrant VIs make a separate copy of the VI in memory for each different place you call them on the block diagram. The separate copies can therefore run at the same time independently of each other. So what you would want would be a reentrant VI that you could instantiate for any number of your signals. The problem is that reentrant VIs in 7.1 and before always shared one front panel in memory, so they couldn't act like popup dialogs. 8.0 and above now allow reentrant VIs to act like popup dialogs by giving them each their own copy of the front panel.
So upgrading is one option. Now, the fact of the matter is that your requirements state that the user should be able to pop up any number of these graphs, but you might ask yourself how many the user could actually view on the monitor at one time. 10? 20? I'm guessing there's some max number the user just can't possibly exceed or even pay attention to visually. So my opinion is that the LV 7.1 solution will involve making some max number of copies of the VI on disk, giving them enumerated names (like subVI 1, subVI 2, etc) and then reusing this fixed number of subVIs cleverly. It's rarely the case that you really need an unlimited number of graphs or popup dialogs.
Jarrod S.
National Instruments