TG3482G router is not seeing my NAS, but the connection is still good. What is needed for it to see the device as online?

Not using a static IP address isn't a great solution - I have some software that writes to this server based on IP/port, so I would need to reconfigure that every time it bounces for any reason. 
If I'm not able to get this working w/out making it dynamic, then I'll need to find some way to handle that.  So, last option there I think.
The Windows system that was working in its place beforehand also always had a static IP for that same reason, and it always seemed fine. 
The MAC address is built-in to the NIC, and I only have one NIC plugged in on this system, so that should always be the same.
As far as I'm aware, I do not have Advanced Security enabled.  If I go to the Security tab in the app, it's prompting me to turn it on.

I'm not sure if it's useful information, but I HAVE found some minor success in creating a new user and assigning the NAS to that.

It had previously been grouped under 'Household' which regularly has 9 or 10 things connected.

I moved it to its own user so I could more quickly monitor whether it was or wasn't connected - and it's since been connected the last 4 or 5 times I've checked.

Is there perhaps some limit of devices a given user is allowed to have connected at once?

Thank you for all of this information, Xenon37.

With xFi, you no longer need to set a static IP for devices you wish to port forward. xFi port forwarding relies on the devices getting an IP address from the DHCP. When adding a port forward, xFi will use the IP address from Dynamic Host Configuration Protocol (DHCP) to set the static media access control (MAC) bind and establish the port forward rule.

I have not seen any device limitations regarding how many can be connected at one time or a relationship if you put the device as a separate user. Have you tried to set this up using our recommended instructions? Our system accounts for it being static and should keep it connected from the IP address in the DHCP. 

I will try setting it to use DHCP instead of Static IP. 

If that works, then I'll need to find some other solution for the in-network applications that connect to it via IP address however.

Is there a way to set a sticky-IP, so the DHCP will continually assign this MAC address the same IP address on restarts?

Thank you for trying that, u/Xenon37! We only offer Static IPs with our Comcast Business service. We do not have a way to set a sticky IP, it would remain dynamic with our Xfinity service. The device's IP would be bonded with the MAC address to keep the port forward working as the IP changes. 

Just to clarify, the static IP I'm talking about refers to a private IP on the network - not a public static IP.
Ie, the router is at 10.0.0.1, and I set the VPN to be 10.0.0.42, my personal computer to be 10.0.0.37, my printer is set to 10.0.0.10, etc.
Nothing set in the router at all saying that it's a static IP or anything - I've just told the device to use this specific IP, and set the primary DNS host to 10.0.0.1 so it's still going through the main router in order to do any lookups, etc.
The public IP can be dynamic - I have a DDNS server set up to handle that routing.

I'll keep an eye on this and see if it works for a day - if this is the requirement for Port Forwarding, then I can probably find workarounds for the other software connections.
It just seems really weird to not be able to set my own local network IP addresses.