It looks like you're misinterpreting things a bit. Desynthesis goes by the item level, not the equip level. So you'll need to desynth things at roughly the same (or not too much higher/lower) item level as your current desynth level. Heavensward lvl 51 gear is item level 115, so that's why you'll be unable to desynth at your current level. Desynth level 70 corresponds to the Darklight gear or otherwise similar item level craftables and dungeon gear.