I'd recommend not using Splunk to listen directly for syslog, but instead have a syslog server (syslog-ng or rsyslog) listen for syslog and write that to files. Splunk then picks up the files and reads them.
This has a LOT of advantages. It is considered best practice. It makes restarting Splunk not interrupt your syslog inputs for that minute or two. It makes troubleshooting easier by separating the two functions. It makes the various configurations involved simpler. It also increases throughput.
And most importantly, I would be VERY surprised if you continued to have this problem after you convert to syslong-ng and Splunk reading those files.
For what it's worth, you can run the syslog server right on that same box.