I have seen a somewhat similar problem while testing vector tiles. The tiles disappear at certain zoom levels - see attached zoning map image where there are large blank gaps. Vector tiles published via Pro 1.3.1.
In our case, the problem is evident on 3 browsers (Chrome, Firefox and IE 11) and on different PCs. Our PCs are anywhere from 2-4 years old (Win7, Dell, Intel Xeon 3.6GHz, 16GB RAM). I have not determined if it is a data problem, but at other zoom levels the tiles display fine.