He told me (as I suspected)
We don't look for an acceleration because the 4 year time period of our altimeter observations is too short to reliably detect this, given the large year-to-year changes in annual mass loss. So I wouldn't say that there is no acceleration, rather that, given its likely magnitude, it is not possible for us to reliably measure it over such a short time period.
For assessing accelerations in mass loss you really need to use the longer 10-20 year records which are better able to resolve this. You may be aware of it already, but in case you're not, the attached paper gives a nice analysis of the time periods required to detect certain accelerations.
I'm not aware of any reasons to expect the long-term acceleration to go towards 0.