In preferences > Network, do you have TLS enabled? Try disabling this. It's disabled by default, but mine was enabled.
I tried two Acqlites running simultaneously on Snow Leopard & Mavericks. Seems disabling TLS 'might' have fixed the issue for me.
Both Acqlites running for 5 hrs without drops in connections.

Edit: one 7 hour session for one Acqlite & two for the other, no connection issues. But the question is if TLS is your problem.