Can drying out be a converter problem? - eviltoast

My Kaco EDGE is drying out, even when using it the next day. I feel that the issue is related to the converter, because usually I can fix the issue (even for a couple of days) by driving the converter just a little bit outwards and then cleaning the pen. The converter is a rather cheap one made of plastic. It came in a set with the pen and the schmidt EF nib. I saw this set of many places, but it looked like this:

https://www.amazon.com/Matte-Fountain-Schmidt-Cartridges-Original/dp/B07HG1J9M1

What is the “right way” to fix this. I know the TWSBI Eco wants to be greased regularly – is this a thing with converters?