I found that when one of our machines reboot, I see audit errors in the event viewer saying that SQL Server Express cannot logon with NT Authority\System, there after my service application gives a similiar login error and does not start.
If I then start my service application manually (with services.msc), it starts perfectly. So the problem is only with rebooting.
So it looks like it is an issue with when the System account is available when SQL server service starts?
I could use an SQL server account in my applications SQL connection string but then would I still have the issue with SQL server express complaining (i.e. the audit error)? Alternatively, should I run SQL server express under another user account rather than local system?