Are you using the Mono package from the official Synology package repository? If so, it is really old (4.x) and is insufficient for Duplicati versions 2.0.5.x and later. It MAY be related to the problems you are seeing.
If you are using mono 4.x then I recommend stopping Duplicati, stopping Mono, then uninstalling the Mono package. Install the Mono package from https://synocommunity.com then restart the Duplicati package.
Had again the same issue:
Connection to server is lost. Stopped the Synology package, started Duplicati server via command line which worked.
Then stopped the Duplicati server again, started via Synology package, again no connection to server possible.
Then stopped the Synology package again, started server via command line, then started a backup task manually, then stopped server and started Synology package again -> worked!
Mono version is 220.127.116.11-13 (SynoCommunity package)
I really wonder what’s happening. At least I have a (although complicated) workaround now…