Arduino + HX711 + 4 50kg load cells - measurement degrades over a few hours

I guess you will have to define what you consider degrading. As for the "oscillation" assuming you really meant to type 0.005 kg, That would mean the oscillation is 0.01%

Welcome to the real world. Nothing is perfectly stable. Most things change with temperature and added noise on low level signals cause issues with a sampling A/D

You will have to define your expectations, and the load cells you are using for a better suggestion as to what is possible and / or what can be done to make it better.