Which ISP are these "important" accounts under? Hotmail, Yahoo, Comcast, Verizon, Roadrunner?
Hotmail. All 4 are hotmail. Can't figure out why 2 work and 2 don't.
There was an issue in the last few days with Hotmail on their server side where multiple people had syncing issues. The link to the Hotmail server status is one or two of the other recent discussions on this community forum.
You can try removing the accounts with the issues and re-adding them again under the "Other" account type or as an Exchange account and see if that helps.