Firstly I noticed that there is one cell with unusually fast voltage drop, when the cell voltage dropped to 3,2V the BMS turned the complete battery of to prevent damage. Removing kapton foil revealed a crack on the battery pouch:
Replacing complete battery is not an option, 6 of 7 cells are still fine. I wasn't able to find exactly the same replacement cell so I decided to cut the corners and built a cell combination which will fit into the place of the damaged one. 6 pieces of 18605 cell fit perfectly and if they are connected 2S3P then their voltage matches original li-po cells and their capacity is even higher than rest of the cells. I ordered 6 new 18605 cells already welded in the desired shape and put it instead of the damaged cell.
My strategy was to fix the battery by replacing damaged component and I believe that as long the new cell has got the right voltage and at least the same capacity (ideally a bit higher) then it has to work.
OZ890 BMS had to be reset to accept the battery. In this case one of the middle cells were replaced, it means, during the complete operation OZ890 was powered up continuously and it detected 0V on one of the cell which was replaced. I wasn't able to reset the OZ890 with original o2micro USB I2C interface, but disconnecting the BMS from the batterypack completely did the trick. After reset the BMS allowed normal charge and discharge procedure. This means, that there is no Coulomb counting in the BMS and that there is voltage supervision only. I don't expect this trick to work with more sophisticated BMSes. Fixing this battery wasn't all that difficult. It has been couple of month since I did it and the battery still serves its purpose.