No, arbitrarily many doesn't automatically mean a huge amount :) This definition covers permanent partitions, but also encompasses temporary partitions which are effectively one dropped message or more. There exist protocols which will be broken by the loss of a single message. Paxos may not be one of them, but there is also a pattern of loss which will break that as well.
The theory behind all this really does hold this point up. I have another blog post with much more detail on the theory here: http://the-paper-trail.org/blog/?p=49, but I warn you it may be heavy going.