Poor sync has been a known problem for a long time on the Monitor. That's because the Monitor locks itself to the hardware that you've connected it to while the rest of OBS uses a different timebase. This allows the two clocks to drift apart, and OBS handles that by growing the buffer ad infinitum. That's a lot easier to code than resampling, especially for someone that doesn't understand DSP code very well (DSP code is weird and not intuitive at all to read directly), but if it's going to be useful with independent clocks, then it MUST resample. So because it doesn't, the Monitor may or may not be useful for you, depending on your system's clock distribution.
You can reset the buffer by stopping the audio to it and restarting it, but that creates a glitch that may or may not be audible. If you're a little bit smart about it, you can isolate that reset and its glitch to only the Monitor and nothing else, by having separate sources for each input that each only go to one place. Reset the Monitor copies and leave the others alone.
Is that what you're asking about? Or is it the Output that you're having problems with? The Output stays within OBS and keeps that clock, and feeds both the stream and the recording. If that's what's getting out of sync, then there's something else going on.
