I have a 4' hose that is closed at one end and connected to a Airdata Test Set (precise control of pressure) and a high accuracy pressure monitor on the other end with a T and valve. The valve allows the Airdata Test Set connection to be closed off resulting in a hose connected to the pressure monitor and closed at the other end. The valve is a high quality needle valve. The pressure monitor is a a Druck DPI 142. Half the length of the hose is in a temperature chamber controlled to 70 C. The Druck connected end is outside the chamber at roughly 22 C. When the airdata test set is commanded to a pressure of 1300 mb and allowed to settle for 30 seconds or so, then the valve closed, the pressure reported by the Druck drops over 20 minutes or so with a decreasing rate of change. The airdata test set draws air from the room when operating. The hose is ~0.190" ID neoprene, Saint-Gobain P/N 06404-15. The temp chamber, hose, etc, are given 1 hour to thermally stabilize prior to commanding the pressure to 1300 mb. The difference between initial pressure and stable pressure is ~18 mb. Why does the pressure take 20 minutes to stabilize?
Firstly, and forgive me for asking the obvious, are you certain that there are no leaks anywhere in your setup? I'd suggest getting someone else to check it over in person - it may be something obvious you've overlooked that a fresh pair of eyes would see. Again, apologies if you've already tried this :-)
Assuming that's not it:
As you increase the pressure in the hose, the air temp in the hose will also increase (work is done on the gas to increase the pressure). As the temp settles back to equilibrium, the pressure decreases slightly according to $pV = NRT$. (I think you say you allow 1 hour for equilibrium prior to increasing the pressure).
If this is true, then increasing the pressure again should result in a much smaller pressure drop (since an increase of 18mb will result in much less heating than 1300mb).
Are you able to monitor temperatures inside the hose?
Given that the pressure does seem to settle, this is where I'd put my money.