Duncan, this is an interesting idea. For the so-called ‘benchmark universe’, matter and lambda, the scale factor, a(t), is proportional to (sinh(t))^(2/3). So let’s try and see what the Friedmann equations look like if we keep this evolution of the scale factor, but restrict it to one component, which I assume is matter.
The universe has undoubtedly lost mass-density since the good old days. That is very much not the same as losing mass. And, as I noted, losing matter is not the same as losing mass.
It is extremely important to be precise in one’s terminology when discussing situations in General Relativity. For instance, it is very tricky to determine the mass contained within a region of spacetime other than in the context of an asymptotically flat background.