Apex Legends has no shortage of various ordinary and less-ordinary errors for players to contend with, though Code 408 harkens back from the days of Titanfall 2.
Apex Legends Code 408 is an error relating to matchmaking server connection or, rather, the lack thereof. It's a bug that results in an immediate disconnect and unlike some others, a simple restart of the game may not be able to fix it every time. We do have a potential solution, however.
Apex Legends Code 408
There seem to be two separate solutions to the Error Code 408, with one being fairly simple but also depending on disabling some of your hardware, and the other a more complex, yet also handier long-term fix. We'll walk you through both, and you can decide for yourself which serves you best.
Error 408 Simple Fix
Sourced from EA's public helpdesk, this solution will require of you to disable whatever sort of Internet connectivity option you currently aren't using.
Go to: Control Panel / Network and Internet / Network Connections, where you'll be presented with Ethernet and Wi-Fi connections. Right-click on the one you're not using and select the 'disable' option. This should resolve the issue.
Error 408 Complex Fix
This solution includes tweaking the Internet connection priority for the machine you're getting 408 on, and it is sourced from How-To Geek, which is a bit of an authority in this regard.
Your best bet will be to follow their own step-by-step guide as it features numerous window captures and thoroughly-explained procedures so as to keep you going in the right direction. What the procedure boils down to is drastically increasing your preferred web connectivity hardware's priority, which should (in theory) allow you to avoid Error 408 in the future.
We hope these fixes help you in your crusade against Apex Legends bugs and problems, and that you get back to playing ASAP.