Apparently there is already a bug report to this 
Let me just drop some stuff here:
I enchanted a claymore (base 10) and it got 11% shock dmg. Then I gemmed it with a fire gem (12%) and that apparently overwrote the 11% lightning entirely.
And I enchanted another claymore (again base 10) and it got 15% fire dmg. Then I gemmed it with a fire gem (7%), so the fire would be 22% total and that increased the fire dmg from 4-5 (before) to 6-7 (after).
So this works.
→ If you have elemental damage on your weapon, only a gem of the same element will keep the enchantment alive!
Link to related topic: What weapon gem to use