I'm pretty sure all golems now take damage even when using a 100% poison dagger with no damage increase. This change was made a few years ago actually and has been a pain in the butt ever since. Your weapon will also degrade and need to be repaired.
If your golem does not take any damage then you have a "pre-patch" golem and it is worth several million on some shards. The answer "get a better golem" is fine but only if you intend to pay for a pre-patch golem.
There are several ways to heal the golem, Oracle mentioned the tinker on a second account. Last time I trained you could also use Gift of Renewal. You can't use bandaids or mage spells.
XII