I've got one that accesses 80 PLCs. I just open a connection, read what I want, and then close (dispose of) the connection. I did have to modify AdvancedHMI to get it to work (See:
http://advancedhmi.com/forum/index.php?topic=366.0), but that shouldn't affect you.
Have you tried reading just those tags that are giving you problems? Do they fail consistently?
And I would recommend opening just one connection to a PLC, reading what you want, closing it, and then going on to the next PLC.
My other AdvancedHMI program reads 40 or so tags at once, loads them into a bunch of LED displays, and goes back and does it again. To make it easy for AdvancedHMI, I bunched all of the tags into a single array in the PLC. Have you tried that?