From the SOAP::Lite docs:

on_fault()

This lets you specify a handler for on_fault event. The default behavior is to die on an transport error and to do nothing on other error conditions. You may change this behavior globally (see "DEFAULT SETTINGS") or locally, for a particular object.

So, you would use:

my $server = SOAP::Lite                                             
  -> uri('http://www.soaplite.com/duplsvr')                           
+                  
  -> proxy('http://my.ip.com/cgi-bin/server.cgi', timeout => 60)
  -> on_fault( sub { } );  # ie, do absolutely nothing
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