It might be full, it does have a capacity limit. Right click the bin , go to properties, custom size, then set it to some bigger size.
Recycle Bin storage size - Vista Forums
If something is in it for over a few days, does it really need to be? It is supposed to be "emptied" on occasion.
I don't know of a 3rd party non-deleting bin.
Maybe you should make a new folder for stuff you don't want, but maybe do. It would serve the same purpose since the files in the bin aren't removed from the system "inventory" until you empty the bin. Only after that will they be overwritten eventually.