A few thoughts on this:
1) Is your PMS machine (the i7) wired to your switch/router? Or is it wireless? If wireless, try it wired to ensure you don't have issues with interference from other nearby radios, garage door openers, microwave ovens or towers, your neighbor's WiFi, bluetooth, cordless phones, etc. You may need to run a temporary cable for this test.
2) Is the TV wired or WiFi? (Do the same for this, for the same reasons.)
Most routers have an option for something like a Site Survey. This tells the router to check if there are any interfering WiFi hotspots nearby that use the same channel. This testing only shows other WiFi hotspots, though, and not other interference issues. Try changing the radios channel to something with less interference. This doesn't resolve the fact that you may have everything WiFi, though. PMS machines should ALWAYS be wired to the router/switch for best playback. As well as any high bitrate capable client devices. Any kind of interference is going to dramatically affect streaming unless it's wired.
3) You don't tell us what file format or codecs the problem files are encoded with, so try to find a file on your system with MP4, H264 with AAC stereo audio and test it playing. You also don't state whether it's a 1080p, 720p or 4K, etc. Keep in mind that transcoding 4K because of a wrong codec or container is likely to take considerably more power from the CPU, and if the i7 doesn't have it, you buffer.
4) Are you Direct Playing or Transcoding the stream? When you start playing, open the Web App, and you should see an orange (some say yellow) icon in the top right of the Web App. This shows that you have something playing, and when you click on it, you can see what and who, etc. There's a small circle with an ! in it that tells you a bit more.
If it's transcoding, it will say if it's audio, video or both. It will say Direct Play if it's Direct Playing. This means it's copying the file straight to your TV without any modifications. Ideally you want most or all of your media doing this for the least problematic streaming. This will take a bit of effort to get your media into this type of condition, but until it is, you can likely expect issues....
5) Do you have any log files from the server that cover a time frame for this buffering you have going on? Seeing those logs can help to resolve your problem. The other 4 points above are just ideas to look at, without seeing those logs. Seeing them tells us a LOT.
There are a lot of things we need to find out in order to help you resolve this. And YOU need to be the source of that information. The rest of us can only make guesses based on what little information you've provided. For more information on what info to provide: https://forums.plex.tv/discussion/195773/troubles-read-here-to-learn-how-to-provide-great-logs#latest and https://support.plex.tv/hc/en-us/articles/200250417-Plex-Media-Server-Log-Files