So GT Sport - like GT6 and GT5, and GT5P - is a bit sensitive to network environments, and a connection that's fine one day (or hour) might be ropey the next. There's an "easy" way to optimise your own network environment and make it as stable and friendly as possible.
Step 1 - Wire it in
A wired connection is innately more stable (and marginally broader and more responsive) than a wireless one.
Step 2 - Static IP address
This is a little more complicated and requires knowing a very small amount about your home network.
In essence, your router (the thing that plugs into the outside world) has a small amount of addresses (called IP addresses) that it assigns to the devices connecting to it. It receives information from the outside world, works out which device it has to go to and sends it there. Your device also sends information to it, which the router translates to show which device it has come from, and sends it out. This is a function known as "Network Address Translation" (NAT). Now you know what "NAT Type" means - the type of NAT currently used. NAT Type 2 is best and NAT Type 3 is the worst, for really boring reasons. If you have NAT Type 3 you will absolutely need to do the rest of this list.
If left to its own devices (it probably would), the router will assign IP addresses automatically. This means that every time a device is turned on, the router gives it a number. This is usually sequential, but not always, and known as DHCP (Dynamic Host Configuration Protocol). If you have lots of devices connected at once, this can sometimes cause issues as a device "wants" the IP address another one is using. It's usually only a hiccup, but it can be bad if you're doing 140mph when it hiccups because your kid is checking their phone...
For stability purposes it's better to assign each and every device in your house its own, permanent IP address. First you'll need to find out what IP addresses your router uses. Usually, this will be 192.168.0.[any number from 2-255], with the router itself as 192.168.0.1, but not always*. Best way to check is to look at the router's own IP address, printed on the back of it. That's the address you'd type into your browser to log into your router's control panel. Once you've found out, pick a number from 2-255...
Then, on the PS4 go to:
Settings (second button from the right hand side)
-> Network
-> Set Up Internet Connection
If you've wired it in as above, pick "use a LAN cable". If not, bad you, pick WiFi.
On the next screen pick "Custom", and then "Manual". Now you need to enter the IP address you've chosen, along with some other... kookier information.
For your IP address enter the number you picked. "Subnet Mask" is even more almost always going to be 255.255.255.0. "Default Gateway" is your router's address. The DNS (Domain Name Server; the servers that change the IP addresses of locations into names, like gtplanet.net) settings are up to you; your ISP has its DNS and these will likely be in the router's control panel under DNS. It's easier to use the free DNS at OpenDNS. These are "208.67.220.220" and "208.67.222.222".
As a random example, the screen should now look something like this:
IP Address - 192.168.0.4
Subnet Mask - 255.255.255.0
Default Gateway - 192.168.0.1
Primary DNS - 208.67.220.220
Secondary DNS - 208.67.222.222
On the next screens hit Automatic, Do Not Use and Test. It'll now do a network test. If you have set ANYTHING wrong, it will fail at the "Obtain IP address" or "Internet Connection" stage. Double check your numbers...
Lastly, it's best to do exactly the same thing in your router, and it's required for the next step. Routers vary wildly in where to find this function, but you should have your own instruction manual for it... It's likely to be under an advanced settings menu, labelled as IP addresses or network configuration or something similar. All you need to do is find your console (this can be tricky, as it may be listed by its MAC address; you can find your console's MAC address in its Settings menu somewhere. I forget where. It's a set of six pairs of hexadecimal numbers, from 00-FF, separated by colons), click on that and enter the IP address you picked for it.
If you think this is geeky, I've done it for every device in my house, numbering 25 or so now. And the consoles, laptops, mobiles and computers are separated into dedicated IP blocs, so when we get a new one it's easy to remember what the next number should be. NEEEEEEEEEEEEEERD!
Step 3 - DMZ
So, basically, devices need to send information out through "ports". This is stupendously difficult to explain - you and I might think that a "port" is what you plug a cable into, but it's not. Well, not in this sense - it's a networking thing. Routers have built-in protective "firewalls" that block certain ports under certain conditions. This is great - it helps prevent your computer from being compromised, or sending out information when it has been - but when a console has its ports blocked, you can't game.
Routers also have a place outside of their normal firewall called the DMZ - which, yes, is the Demilitarised Zone. This is a connection where the firewall doesn't exist, so there's no defences. As there's no defences, there's no ports blocked. This is great news for gaming.
Once you've assigned the static IP address to the PS4 both in the console and in the router, you'll want to find your router's DMZ function. Again, this varies wildly, but is often just labelled as "DMZ". It may be under a Firewall menu or similar. Again, consult your manual. You'll need to then assign the console's IP address (or some routers allow you to assign the device, if you can remember its MAC Address, or you gave it a name) to the DMZ.
You can only assign a single device or IP to a DMZ, and your console is the safest thing to put there.
Once you've done all this, the chances are that you won't see any immediate differences in the network test. You might have a slightly lower ping, or a slightly higher bandwidth, but probably won't. But what you will have is the absolute ideal conditions for your console for online gaming, and the only disconnects that will affect you should be when everyone gets booted from a lobby. Or if your internet connection itself falls over, or there's a power cut.
It won't cure low bandwidth, high ping connections, but it will make it more stable and it's everything you can do to make it work. Unless your ISP throttles gaming traffic, which some do, the bastards...