Seems to me a little investigation into the (many) ways rsyslog can be configured is in order here. It can be relatively simply configured to ship logs asynchronously, and reliably, to a remote log server, and buffer them on disk / in memory in the event the remote server is down. This is what we're doing, and it works very well.

http://rsyslog.com/doc/queues.html

http://rsyslog.com/doc/rsyslog_reliable_forwarding.html

(This isn't, however, to say the documentation on this stuff is easy to find / understand. The rsyslog documentation is definitely not the best.)