Sorry, freak accident with submitting the form.
I don't know of any issues with using fsockopen multiple times. You might run into long load times and so you may want to set blocking to false with [man]stream_set_blocking/man, and if you're doing a bunch of streams, you could use [man]stream_select/man to iterate over all the streams that you want.
The only issue I see you running in to is maybe lagging your script (or potentially timing it out) with so many connections. That limit is more than likely dependent upon your system and what it can handle, so some trial and error might be involved.