I take a video file, let's say an mp4, and use, let's say Windows Movie Maker, to repeatedly just save it, with no edits. Every time, the software has to convert the video into a format it can edit, and then convert it back to an mp4. Will the repeated conversions begin to degrade the video's quality if I do this over and over?
MP4 isn't an ideal format for intermediate saves. If you know you'll be re-opening the file, save it as losslessly as practicable, and use MP4 only for the final output.
That said, depending on the encoder and settings you probably don't lose much if anything on subsequent saves. MP4 and similar codecs work by decimating the higher frequencies (details, resolution) in a predictable way. Once you've saved an MP4 at a particular quality setting you've already discarded the information. If you save again using the same settings, there's no information to lose in the areas that have already lost it.
If the codec is not lossless, such as Quicktime Animation Codec; true lossless, then yes.
But if you are using a good encoder, I would gather even after 100 generations of degredation would you be able to even visually see the difference if you continually re-encoded the file outputs using MP4 at a high bitrate- say 30mbps for 1080p.
Lower bitrates, yes.
Yes. By definition, any time you save an audio or video file using a LOSSY compression scheme, you will lose something (by definition).
Now, modern codecs have been getting better at minimizing perceptible losses. But it is always preferable to avoid ANY extra compression steps. Until the project is completely finished and ready for distribution, it is best to keep it in an UNcompressed state.
All codecs, unless they are truly lossless, suffer from concatenation errors. Every time you encode with a codec, decode, and re-encode with the same or a different codec you will degrade the quality of the video. It isn't as precise to figure out just how bad it will be as when you could count the generational loss of re-recording to tape as the source and destination codecs affect the number of cycles before the artifacts become noticeable.
When you perform an export from most editing software, even if you don't change anything, you go through a full codec cycle. The software internally decodes to its native format and then re-encodes to export. This means that it will interpolate the discarded information.
In my experience, H.264 (the codec used in an MP4 and that is used Windows Movie Maker) exhibits noticeable to the untrained eye concatenation errors after just one codec cycle.