Brother Hl-l3230cdw goes offling

First thing I would do is reset the network settings to factory - every networkable printer I have worked with it has it. It's usually under the network settings, typically independent of the main reset. The factory reset often misses the network settings. After you do that, see if the IP is DHCP or Static - if it's not static, give the printer a static IP from the router side and printer. Lexmark and HP typically put it under TCP/IP where you can take the IP from the printer, make it static and use the IP and use 255.255.252.0 or whatever the printer assigns -- make both static on the printer, then set the IP static on the router, the subnet mask isn't critical on the router side.

One last thing you can try is disabling IPv6 -- it usually isn't the cause but if the IPV6 routing table is poorly implemented disabling it on the printer might be enough to get it going.

If you've set the IP and subnet static, disabled IPv6, check for a WiFi inactivity window as well as other parasitic "power saving" features like it (see: Wi‑Fi Optimization, Eco Mode, Power Saving, “Smart Wi‑Fi”). It's probably there, but most consumer ISP routers lock this out (or limit how much you can change it) for some reason so there's no way to stop it if the connection is being dropped to the point the only way to fix it is to reboot the printer. A lot of these "modern" ISP routers (and Eero in the US, retail and ISP locked) are known to not let you adjust the ARP settings, or even disable the 2.4/5/6G band merging. It can usually be turned off but over time more and more of these ISP tier routers are keeping it on permanently and taking the option away. The band split issue is a BIG one because not all printers do well with it, and ARP adjustments sometimes need to be done because they can break things as bad as you see here. The issue is ISPs see locking these out as "feature" when it's nothing but trouble.

If it continues, your router is shutting things down from inactivity. Keep the static IP (release it from the WiFi and move it to Ethernet), put the printer on Ethernet and disable the WiFi if Brother doesn't shut it down automatically. Routers typically do not "shutdown" Ethernet connections like WiFi, so Ethernet is always better for use with printers whenever possible. The deep sleep mode on Ethernet still has a minor delay, but it's far shorter then WiFi where you often lose the connection. This also lets you work around any ISP imposed limitations they set on the router firmware as you can use a small L2 or L2+ managed switch (L3 is extra, but I've used them - the main difference is high level routing to the internet) from a vendor like Netgear, EnGenius or UniFi (Ubiquiti) to configure the behavior of the printer at the switch level to bypass the Telstra firmware issues. An unmanaged one with automatic routing will work but if it still goes haywire you can't tweak things. Any cheap Cat6 or 6a cable will do -- even surplus 5e. I use cheap UTP Cat6 on my MS621 and color MFP and they run fine, printers do not need Cat7 STP.