Kate - There is no way to identify your Paph with an exact name, but it is a Maudiae-type. They are among the easiest to grow. It looks basically healthy in that pic.

I don't see any major problem with what you are doing except possibly overwatering. It is hard to judge someone else's watering because it depends so much on temperature, humidity, type of media, etc. but twice a week along with root problems probably means too much water and media breaking down quickly.

It should never dry out completely, but wait until it is dry on the surface at least before you water again, and make sure it never sits in a puddle of water. Twice a week may be way too much at some times and not enough at others so don't make it a rigid schedule. You may be able to learn to tell when it needs water by how heavy it is when you lift the pot.

I would also cut back on the fertilizer except when you know your plant is healthy and growing. The plant can't really use the fertilizer unless it is healthy, and it might contribute to problems.

What is it potted in now, and when was the last time you repotted?