If you edit the settings on each device can you get a successful test on the TEST button for the configuration. Are you logging in as a local account or TACACS?
If it is a local account, you might want to make a separate local account on the switch for Solarwinds NCM.
Do you have reporting emailing you a report of the backups and changes nightly?
Some older Cisco switches have issues memory issues in older IOS's (Memory Leak) that will make it so no one can log into the decive unless the power is reset. Update IOS on the device and try again.
RT