I have the same boat and it is turning 10 this year. How about some more info, what is losing air - the floor, a side tube chamber, the entire boat? How long does it take to get soft, days?, weeks?
Aire valves can loosen over a long period of time allow air to escape around the outside perimeter of the plastic valve body. Also some sand/grit can keep the inside of the valve from sealing properly. Both can be checked with soapy water. Put a couple drops of dish soap in a squirty bottle. Make sure the bottle didn't previously have some nasty chemicals in it. Blow up your boat and squirty the soapy water around each valve. If there are leaks there will be bubbles coming from the edge of the valve body. Simply take your valve wrench and tighten up until it stops.
If that isn't the problem, squirt a little of that soapy water into the actual valve. If bubbles occur inside the valve hole then there is likely some grit in there not allowing the rubber gasket to seal. With the boat pumped up to full pressure, push the valve in a couple times to allow a big burst of air to come out. This usually will blow out the small piece of grit causing your issue. Or you might have to swab around inside along the rubber gasket with a q-tip.
If it isn't any of the air filling valves, and its the floor that is leaking, then it might be the pressure relief valve. Squirt the outside of the PRV valve and tight if needed, and squirt some on the inside. If it is coming from the inside you can clean it. But PRV valves can notoriously be bad. Aire has been replacing a bunch that were from a bad batch. If you call them, they would probably send you a new one for free if its from 8 or 10 years ago.
99% of the time a very slow leak in an Aire band boat will be fixed by tightening or cleaning the valves. If not, you have a pin hole some place.