I am not sure but I think the problem is the frame rate. If the in-game frame rate is higher than 60 fps you could experience some troubles.
I played Saints Row 4 with 60 fps lock for about 20-30 hours and experienced somewhere about 2 permanent freezing. Before that this problem was almost every game session. Maybe the 55-58 fps lock will be even more stable. Of course if it causes the problem.

Now I will show you some simple solutions but you could use your own knowledge.
Before we start l suggest you to enable fps counter through the Steam settings to know what fps you got in games.


For example I noticed that in fullscreen mode the game runs at 60 fps and in windowed or borderless mode it shows 120 fps in my case. So choose fullscreen mode and restart the game to apply change.
If it doesn’t help you also try to enable in-game V-sync option and check your fps counter if it works for you.

Or you could change your max frame rate for the Saints Row 4 through the video driver control panel. Here example for Nvidia users:

Use the ADD button to find saintsrowiv.exe on your PC if it is not on the program list.


And for AMD users, this is the old method to use to lock and change FPS:


For all other users of AMD Radeon Adrenaline 2020 version and newer, the steps are different. Technically, for this version, there is no FPS locker, so in order to use it, you will need to use Radeon Chill. This is not really as good as the older slidebar, as shown in the above method. Radeon Chill is found under Gaming tab in Radeon Adrenaline:

For AMD Radeon Adrenaline 2020, you will need to go under Gaming tab, then select the specific game to change. Do not use GLOBAL SETTINGS as this will change all your games, which is something you do not want to do. NOTE: You may have to scan your pc if this is the first time installing AMD Radeon 2020, or if you just installed Saints Row 4 on pc. After the scan, the game will appear in your list of games found under the Gaming tab.

Once you select the specific game, in this case Saints Row 4, click on it and a new menu will appear with many settings. In here, you will want to enable Radeon Chill and it will look like this:

NOTE that the image is showing how to change it for all games, but we only want to change for one game, Saints Row 4.

By changing the sliders under Radeon Chill, it is possible to set it at anything. Since you wish to limit the FPS in the game itself, you will want to set it to a specific FPS on maximum. Since you want to limit it for this game, a good spot to try for is either 60 FPS or lower. This means you will also need to change the minimum FPS. I suggest putting it at 50 FPS. NOTE: This may vary depending on your machine or depending if you have v-sync on or off. If this does not work for you after experimenting with it awhile, continue reading on. Also, make sure to turn these off if you are going to read below and try the next method.

If you still experience permanent freezing in the game after all manipulations check another guide with a different solution by disabling some cores of your processor. https://cs2bus.com/sharedfiles/filedetails/?id=1710785774
Also I want to thank RPG Gamer Man for his guide. Because it led me to this solution. When you slow down your PC by disabling some cores you decrease the framerate.