Here’s two support documents for running Plex on Synology DSM 6. Definitely worth a read.
Synology FAQ (DSM 5 & 6) - Questions, Answers, and a few How-To’s
Installation & Setup of Plex Media Server on Synology
Check out uptimerobot.com.
You can configure it to monitor your Plex remote access port, and will send you an e-mail if it cannot reach your server. Default is to check it every 5 minutes. You can change the interval if desired. The free account can monitor 50 items.
Screenshot from the web page:
