1 -- Both accounts are IMAP and deliver to their own PST file?
{File -> Account Settings -> Account Settings}

2 - Both accounts are in the "All Accounts" Send/Receive group
{Ctrl+Alt+s}

3 -- In "All Accounts", both are enabled, and have the same options set?
{Ctrl+Alt+s. Select the "All Accounts" group and [Edit]}

4 -- While viewing the Spectrum Inbox.
Sync All {F9}
No errors, but no new email shown?

5 -- Right click the Spectrum Inbox in the Folder Nav pane and choose "Open in New Window"
{View -> Navigation Pane -> Normal}

6 -- Does just switching windows (instead of changing Views) force a sync and you see new Spectrum mail?

7 -- ScanPST the Spectrum PST
Repair Outlook Data Files (.pst and .ost) - Microsoft Support