Really sorry for the late reply
@xNovaBattlex,
You could try testing on a single card and compare your logfile to your SLI attempts, if it clears the issue up then maybe it is an issue with current nVidia drivers, SLI &/or the NVENC codec? If not that, then maybe OBS Studio has an underlying issue with SLI support and the way the 1000-series nVidia cards work with the NVENC codec?
If it doesn't make any difference, then I am completely lost other than your CPU is pretty close to the limits which might induce an issue with your connection quality? Does not really explain the 30-60 minutes then fps drops issue you are having...
Maybe someone else will take a look at your log and hopefully have some more ideas...
To note: I have never experienced log entry repetitions like below, only several attempts to hook into games when running MSI Afterburner & ReShade on Battlefield 4 (Takes 5-6 attempts on average, maybe having to go through Battlelog [Webpage execution for multiplayer, haven't tried single player with recording] is the root cause of this issue?) So I have no idea what is going on there as they are throughout your logfile.
In your logfile there are also repeated lines, sometimes a lot of them, for example:
22:23:25.146: [game-capture: 'CS'] capture stopped
22:45:41.893: Last log entry repeated for 931 more lines
<----
22:45:41.893: Device 'Focusrite USB (Focusrite USB Audio)' invalidated. Retrying
22:45:44.908: WASAPI: Device 'Focusrite USB (Focusrite USB Audio)' initialized
23:51:54.055: Last log entry repeated for 795 more lines
<----
An issue with your 'Focusrite USB Audio' driver? Perhaps the version you are running are not fully compatible or potential conflict?
The below error points directly to your GPU/ GPU NVENC I believe:
18:24:33.828: [game-capture: 'CS'] d3d9_shmem_capture: GetRenderTargetData failed (0x88760868)
<--- Repeated multiple times.
18:24:33.831: [game-capture: 'CS'] ----------------- d3d9 capture freed -----------------
18:24:35.804: [game-capture: 'CS'] d3d9 memory capture successful
18:24:35.815: [game-capture: 'CS'] memory capture successful
19:33:47.502: Last log entry repeated for 141 more lines
Maybe there is an issue with SLI after all? Apparently from reading other forums the above error code is for DEVICE_LOST, so your RenderTarget being your GPU (Bit of speculation, It is getting quite late here) is not being utilized at the time it is being called upon by OBS for recording/streaming (Speculation here once again) This one is for the devs to look into to determine if the issue is nVidia or in OBS Studio itself, maybe others with SLI configurations can assist with their logfile uploads.
If not an issue with nVidia or OBS Studio, then it is your game not being main focused window/application when OBS Studio is calling upon your GPU to get the data it needs to record/stream (Speculation) This means a task is running behind the scenes grabbing focus/priority (more or less similar to alt-tabbing out of the game to your browser) which is causing your GPU to enter idle state (Again, speculation) This in turn falls to you to figure out which background task is causing the problem.
If I am incorrect as to the information I have provided above, please be constructive and provide the correct information, to which I readily apologize!