Gradually FPS Drops

Hey! 

I will preface this by saying that I really don't know of a solution (at least as I am writing this). However, I will tell you that I am also experiencing that exact same problem that you are describing! As you mentioned, the game will start with a high frame rate and gradually as you play it slowly dwindles down (as low as 25 fps, a far cry from the 144 fps I would when I first start up the game). Restarting will help but then the same issue will repeat.

Before anything, make sure you did check the following, maybe you have or haven't but it doesn't hurt to double check!

• Make sure your device isn't overheating (there are many programs that can tell you but I find HWiNFO is pretty solid at giving you the information you need). If it is, then you can move on to physically fixing that problem as that would be a hardware issue then. At least for me I haven't seen any thermal throttling issues, especially with the GPU/CPU utilization pattern I'm seeing, more on that later...
• Ensure that Apex is actually using your dedicated GPU, or at least force windows to use it!
• Some other tips: Turn off xbox game bar if you don't use it, make sure background apps aren't on since that can also pose some performance issues, make sure that you don't have other apps that open up when you boot up your PC as they'll end up in background running without you even noticing (this is slightly different than disabling background apps).
• Reinstalling the game should also be one of the obvious steps to try.
• Make sure that you have updated your graphics drivers and other important system software!
• Perhaps trying changing from DX12 to DX11 (-anticheat_settings=SettingsDX11.json). At least on Steam you can do that by going to Library > go to apex > click the gear > Properties > General, and then paste that into launch options! Perhaps that might work, it didn't for me but it's worth a shot.  

Now, you did mention changing the actual graphic settings in the game, so good job on doing that (sometimes it's nice to be reminded to do so).

I have been looking a bit deeper into this problem and at least for me if you open up task manager on another monitor you can see that the utilization of both the CPU and GPU gradually decrease over time as well which is... odd. You can also check for yourself if this is the same thing you are viewing. If so, then unfortunately the only thing I can tell you is that this might be an issue with the game and who knows when that will get fixed.

Hopefully one of the tips help! If not, then maybe someone else can help. I don't know it all, just a fellow soul trying to help out!