There remains a question of semantics, which is simply, what is meant by the "observable universe." The fact is, different people are going to mean different things by that very phrase. Indeed, the Wiki on the "observable universe" contradicts itself in its very first paragraph, stating first that "The observable universe is a spherical region of the Universe comprising all matter that may be observed from Earth at the present time, because light and other signals from these objects have had time to reach Earth since the beginning of the cosmological expansion", but then four sentences later it changes its meaning, saying "Every location in the Universe has its own observable universe, which may or may not overlap with the one centered on Earth." So they seem to pick a particular universal age for their meaning, but not necessarily a particular vantage point. But note that in this meaning, there is no way to answer how it changes with time, as it exists only at a single time.
This meaning gives us various choices for how to extend the "observable universe" forward and backward in time. For example, we could take all the stuff in today's "observable universe" from Earth, and ask where that stuff will be in the future, and where it was in the past. Then we can use language like "when the observable universe was the size of a grapefruit," etc., but notice the ambiguity: when applied to the future, like "what will the observable universe be at such-and-such a time," we invariably imagine updating what could be seen by the beings of the day, but when applied to the past, we generally don't imagine there are any beings at all, so we don't update what their observable universe would be, we take our own and just shrink it.
So quite frankly, the term is really something of a mess, and so to answer your question, we would need to clarify which meaning you are taking. Let's assume you mean the "obserable universe" that is constantly updating what hypothetical beings could observe had they existed on Earth at the time, then we do have a time-dependent mass. As the Earth ages, there will be more time for light to reach us, so the observable universe will increase in size, but it will not necessarily increase in mass. Assuming the acceleration continues as expected, the observable universe mass will increase by something like a factor of 2, reach a maximum, and then begin to decrease. Its size will always be increasing with time, but its mass will then be decreasing.