This tube-swapping thing turned out to be a quite interesting story.
First, a little background. I'm renting an "abandoned" studio on monthly basis. The studio owner is not using his studio at all, so I'm there on my sparetime doing some recordings.
So, this AKG SolidTube that I had problems with, belongs to the studio. Tonight I walked to the studio to pickup the SolidTube mic and bring it home to swap the tube. But, there is a locker in the studio containing various spare parts. I have never really had a reason to find out what kind of stuff that hides in there. But tonight, I thought that I could take a look for some tubes in there.
Bingo! I found four old Telefunken ECC83 tubes. I have read that these tubes should be quite good. So I opened up the microphone and pulled out the bad tube. And it seemed like this microphone already had been modded because it was a JAN Philips 12ax7WA inside it (also a good tube from what I have heard). And suddenly, some things about the AKG SolidTube started to make sense. This microphone doesn't have a good reputation but I have always used as my go-to vocal mike. And the tube sitting in there is probably the reason to why I like this mike.
Anyway, I swapped the tube for a Telefunken and now it seems to work fine again. I didn't have time for some serious testing tonight but it seemed to work well.
Thanks for all the comments and good advices in here. I will probably write more when I do my next session with this microphone. Maybe some of you are interested... I don't know...