Hi there! This sounds exactly like the issue some of us have been facing for a long time. There are several threads about this particular issue, but it seems no one managed to find a fix for this.
https://obsproject.com/forum/thread...preview-which-goes-into-recorded-videos.77744
https://obsproject.com/forum/threads/frame-rate-is-cut-in-half-stutters-every-10-minutes.39269
From what I've understood, this problem is external to OBS. The same stutter shown in the preview every 10-15 minutes also goes into the recorded videos and, at least in my case, no lagged / skipped frames are logged by OBS. It seems there's some kind of prioritization bug involving Windows DWM or DirectX, that results in the capture of duplicated frames by "background" processes like OBS. These repeated frames are the source of the 'stutter'.
I even tried fiddling with the OBS source code, specifically the parts which affect the 'Desktop Capture' (Desktop Duplication API), but it only made things worse. From my testings, I concluded that everything that uses DirectX 11 to hook / capture frames (Game / Window / Display Capture) would eventually begin stuttering after some time.
Maybe the use of a different source, like acquiring frames of a capture card through DirectShow, will bypass this issue. But I'm not 100% sure about this...