Edit: Before you go through this I just realized you're running Plex off the Diskstation. The DSj411 has a really weak CPU and it could be taking a long time to process the metadata. I would recommend moving Plex Media Server off the Diskstation and onto your PC. Once you do that map the drives like we've been describing.
Ok so what is likely happening is the computer's name is being lost in the network. When a machine joins the network and gets a DHCP address from the server/router the name of the new device is stored. Sometimes though the network can hiccup and the name is dropped. (I'm being super generic here).
The best thing to do would be set a static IP address for the Synology server through Diskstation. First thing to do would be get proper IP information and then find an open IP. Open up a command prompt (Start>run>cmd) and type in ipconfig
You'll see your computers IP address, subnet and DNS information. It should read something like: IP: 192.0.X.X Subnet: 255.255.X.X DNS: 192.0.X.X (X is a variable based on the router you're using. Some use 0.0 and some use 1.1) Gateway should be in there too
Pick an address far out from the last digit IP. So if your IP is 192.168.1.12 pick 192.168.1.100
Verify it's open by typing 'ping 192.168.1.100' in the command prompt (minus the ' )
If it says no host/response you're good. If it responds then pick another one (101 or 99) until one is open.
Leave that window open.
Log into DSM (FYI I'm using the live demo from Synology as I don't have a Synology product)
Go to Control Panel > Network > Network Interface
Click the one that is Blue (active) and hit Edit
You'll see the boxes for manually setting an IP address. Enter in the information based on the previous info gathered. IP == the one you picked (192.168.1.100 for example). Subnet mask, DNS and Gateway should all be in the command prompt from when you did ipconfig. If you don't see it type 'ipconfig /all' (minus the ' )
Save it when you're done.
If done properly you should have a static IP address for your Diskstation. This means no matter how many times you restart it or whatever it will always be that IP address.
So now when you do a UNC path in a mapped drive instead of doing //diskstation you can //192.168.1.100
If you'd like to still use Disktation for a name with mapping you'll have to edit your Hosts file. This will tell the computer that whenever you type 'Diskstation' into any explorer window it will route to 192.168.1.100.
See this for a quick tutorial on how to do that:
http://www.tomshardware.com/faq/id-1821155/edit-hosts-file-windows.html
If you edit the host file just map the drive with that new name.