Sounds like a wire has come lose or snapped inside it -- if there is a weak connection the resistance will be higher hence the lower volume and also noise as you are possibly shorting something else out or making and breaking connections many times a second). Moving the jack can also be a signal of the socket in the speakers/player/laptop/whatever is in need of some attention (usually it is dirt inside it, can be something more though) but if it does it in multiple devices then it is less likely to be many failed sockets.
Heaphone wise the usual suspects are crappy build (11 dollars is very much in that price bracket), abuse (do you pull them when you move on your chair or anything?) and dodgy design (
http://static.bfads.net/size/250x25...-Pro-3000-Headphones-Ass-BFAds-1382709236.jpg does not look the best I have ever seen).
That it happens when it is near the jack is not unexpected as it probably has less strain relief and a better fixing than the other end. You can chop a bit of the wire off and put on a new one if you want (or replace the whole thing), do note that if you are soldering headphone wire then they are usually enamel coated so remember to get rid of it (I prefer fire, if you are boring and want to clean your soldering iron then you can also try solder (put it in a molten blob, lose the solder after that and use fresh) and if you have fine grade sandpaper (800 min) you could try that).
