Thank you everybody for you responses - really helpful!
And yeah - doesn't matter with the whole succulent thing, I don't claim to be an expert at all, I just did not want to mix up or confuse the pilea with other plants. I guess you can categorize it as succulent in some ways!
Anyhoo: I did what you guys said, repotted it and everything. Instead of using sand (thank you for that) I smashed a couple of Leca balls (I don't know what you call these in the states?) to tiny bits and tried mixing it with soil creating a more "airy" atmosphere for the plant. Also, another guy on a Danish forum advised me to water it well, soaking it and checking for "bubbles" in the soil to make sure the ventilation is good. I now let it dry out and then water it throrougly instead of doing the "a little water but often"-thing I was up to before.
It seems to do better right now, but it might be to early to tell. Moving it back into a sunny west window also seems to help.
For now, thank you!
