Your videos on you tube are helpful, I just couldn't find my style.
This is a 15-177 Pivot Shoe, which uses our Series 152 Coil Balances. Watch the video below that shows how to remove and replace coil balance systems; while it's for a different Series, the principles should work the same way. If the window isn't staying open, the springs are likely broken and should be replaced. Look for stamps on the springs that indicate what spring weights to select. If there are no stamps, or you are uncertain, obtain the exact weight of the window sash. Give me that exact weight, and we can work out what you require.
These coil balance systems are modular, meaning you really only need to replace the damaged components. However, I think it's sometimes best to replace both springs anyways just to ensure they both have the same spring weight; otherwise there could be problems with one side of the window having a stronger or weaker balance force than the other, which leads to poor window regulation. If the window weighs 10.6 pounds, use the S152-5 5 pound spring. Use one of these on each side of the sash, for a total of 10 pounds of support overall--being within 1 pound of the exact sash weight works fine.
These coils connect to the 15-177 shoe with a 33-072 screw. You can then use the housing components 15-143, 15-144 and 15-145. These sandwich around the coil spring.