By chance, I work on a project that does just that with 18,000 network elements :-)
I don’t believe you’ll find a product that will solve this for you.
What I believe is the way for you in this case is to periodically run scripts that copy these logs to you for a machine your location, and then vc Automatize your analysis of these logs yourself.
If the machines you run are more or less the same type, it will be a very easy service. In my case, the work is quite complicated because there are hundreds of different types of machines, some running operating systems that I’ve never even heard of ;-)
Filezilla? Given the suggestion, I’m not sure this question is appropriate for the site. See relevant discussion at http://meta.pt.stackoverflow.com/questions/57/devemos-acceptances
– bfavaretto