From what I could see the application-log didn't say much besides some certificate problem.
But the bpbkar said something about timeout for the nsf listed above from the activity-log??
The sizes of the ones not working for server 2 (max2k3). I reckon if we find the solution on that one we can apply the same solution to server 1.
BBKristinehamn.NSF 4.44 GB
insatserkristinehamn.nsf 20.2 GB
insatserkristinehamn2012.nsf 9.61 GB
LogMaxiMilia20120521.nsf 3.97 GB
RHKristinehamnKopia.NSF 3.29 GB
statrep.nsf 6.25 GB
BBStorfors.NSF 1.16 GB
Other databases seems to be backuped up, at least they don't give any error.