I can't help with this specific problem but I know how you feel. It happens occasionally with a number of plants. My original potting up of 55 Gentiana depressa eventually left me with just 1 which is now doing well but I've no notion why the others all gradually died off. Everything seemed to be right; compost, moisture, time of year etc.
Having said that, I've never had a seed or self sown seedling from any of my origanums, even the apparently prolific 'Kent Beauty.' I do them from cuttings and have exactly the same problem. They root well and when potted on, gradually die off. I've tried doing a single cutting into a small pot and they don't like that either. The one exception has been O. microphyllum which does grow on nicely after potting the rooted cuttings.
My O. rotundifolium is the original type plant collected by Albury, Cheese and Watson in 1966.