For what it's worth, although I don't have a QNAP, I do have a Synology NAS and had similar issues with accessing it from my Mac computers (Windows PC's were OK).  In my case it had to do with the SMB implementation Apple uses, it's non-standard/proprietary, so rather than using the standard libraries everyone else does, they rolled their own...  While people are always saying AFP (Apple's own legacy networking protocol) is "on its way out", I've found it still the most reliable way of connecting to a NAS with a Mac computer.  

When I setup my eero, I found the 'advanced' setting to configure the DHCP range to start with 192.168.1.0, which is what my static-IP-configured NAS was expecting and consistent with how I am used to accessing my home network.  And in my network I have all DHCP assignments starting at 192.168.1.100, reserving everything below .100 for static assignments, for things like my printer (which definitely prefers a static assignment) and my NAS.  That has also helped.

Regarding Apple computers networking issues, in the realm of 'tweaking-techie' things might be to change the version of SMB that your NAS device uses -- SMB 3.0 is the latest standard but people have reported better compatibility with Apple products by lowering the SMB level used in the NAS to SMB 2.0 or even 1.  You might also look into configuring your NAS to be the 'master browser' on your network (you'll have to google this one) to resolve DNS issues.

Net/net, I think it might be worthwhile to look into setting up a static IP address for your NAS, and always hitting it from your computers using the IP address rather than by NAS 'name'.  So something like afp://192.168.1.50/your_share (for Apple) might give you more success, avoiding local DNS issues altogether.

Also, if you want to use server names instead of IP addresses, try afp://yourNAS.local/your_share.  The ".local" part is apparently important for Mac. 

One last suggestion is that once you set your NAS up to use a static IP address consistent with your DHCP configuration (the same first 3 numbers in the IP address scheme), you could edit your local HOSTS file on your PC to add an entry for the NAS.  Your machine will always consult a local HOSTS file first before attempting to use a DNS entry to resolve a server name to an IP address. 

Again, this is techie stuff but unfortunately important to know because unfortunately networking is almost never a plug-and-play affair anymore...

I have several QNAPS that I use with Mac computers, and this clearly sounds like an IP or DNS issue.  If your QNAP says it has an IP address of 192.168.1.x, there's your issue, since Eeros default to 192.168.7.x, and for any device to be usable it must match the Eero's gateway and IP range.  Seems it's retaining some IP config assignments in use from your old router.  Try doing a basic reset on your QNAP, which will reset all of your settings to DHCP (hold in reset button about 3 seconds or till it beeps once).  I didn't see you state which model of QNAP you have?  Most QNAPS have a small recessed reset button in back you access with a paperclip.  Alternatively, if that doesn't work, you can set your QNAP to a static IP with your old router with a 192.168.7.x, just make sure the address you choose isn't in use.  It of course won't be visible with the old router once you make this change.

I'd also make sure you set your DNS server to obtain DNS automatically.  If you manually assign it, use your Eero's gateway (192.168.7.1) and you can also add a Google DNS like 8.8.8.8.  Then save that config, and then hook up your Eero.

Both the IP and DNS config options are on the same page - go to Control Panel--->Network.

I'd try the soft reset first and only go to the second method if it doesn't work for some reason.  The soft reset should set both your IP to DHCP and your DNS to obtain its server automatically.  Do the soft reset while it's connected to your Eero network.  If you soft reset it while connected to your old router, power down your QNAP completely before connecting it to your Eero network, and then power it back on to ensure it can obtain proper IP and DNS settings.

Hi, I just wanted to leave this here for other people who search for 'EERO SAMBA' and related problems. I installed my Eeros (amazing product! entire network up and running in minutes!) and I couldn't see my Linux Samba fileserver. It turned out I had hard coded IP addresses in my /etc/samba/smb.conf. The line was 'hosts allow 192.168.1. ' and my Eero network had changed to using 192.168.4.x I simply changed the line to the new IP addresses 'hosts allow 192.168.4.' , then 'systemctl restart smb' and it worked. Most NAS are running Linux and Samba under the hood and may have that setting somewhere in their config interfaces.

Was struggling with not seeing my server for a while. Finally found the solution! :) 

In the eero app: Settings > Network settings > DHCP & NAT > Bridge

My QNAP NAS was disappearing from my home network every couple of hours unless I manually refreshed the IP address from the QNAP interface.

I fixed this by enabling IPv6 from the QNAP networking settings and by turning on port forwarding for the NAS from the Eero app. Haven't had any problems since.