iCloud mail keeps showing up even after deleting them

Hi,

My wife iCloud emails keep showing up on Mail even after deleting them. After a few days, they finally disappear but its a little annoying for her. Also, sometimes the emails do not show up on the preview portion of the program until she quits the program and restarts and they appear. Her Earthlink account which is on Mail along the iCloud account acts normally.

I have checked the settings and believe everything looks good. Any one seen this before with any suggestions? Thanks.

Working from 2014 iMac 27"

Jack