Pro res render issue? appears at random

Try transcoding to ProRes outside of Adobe applications.  If running macOS, right-click the MP4 file in the Finder and choose Encode Selected Video Files.  When the options appear, choose ProRes.  If running Windows, try Shutter Encoder (recommended donation it $10), selecting ProRes as the format for export.

Something else to try is rendering an Image Sequence from the the MP4 source footage in After Effects.  If the picture breaking up is intermittent, it may require rendering problem frames individually until a full, clean sequence of frames is created.  The resulting Image Sequence can be used as-is or converted to a ProRes clip.

Part of MP4 shananigans is that sometimes we have a source clip that won't hold up to anything other than playback in which case we can attempt to screen record it to something that's somewhat usable.

1080p30 ProRes 422 HQ is about 1.3GB pers second.  For an intermediate format (that is, a format that's good for editing), that's a modest file size/storage requirement.  When a video format's files size is small, that typically means good for delivery but not good for editing.

It is more likely an issue with your highly compressed MP4 footage. MP4 footage only contains a few real frames. Most of them are interpolated so any decoding problems can result in glitches. You might try just using the Media Encoder to transcode the footage. It seems to have better luck than running it through After Effects.