Cannot connect to Gmail server via IMAP

Edit Subject

everyday i come home and check my new eM client program which i like i see that the mailprogram has an error on the screen that it cannot connect to my 3 gmail accounts i have configured and setup as IMAP accounts.

The only reason why i am thinking that my 3 gmail accounts are giving problems is that i also use my iPhone during the day to check my gmail every 30 mins.

This prevents me from buying this program since i never got these connection errors when i was using Mozlla Thunderbird.
Does somebody know why i get this ?

New emails do show up in my Inbox, so emails appear...but it looks like if there are sometimes connection errors (maybe my iPhone is also connecting at the same time ?) but then i expect that these windows do not stay there on the screen.

See below a screendump...

I have to select a related product on the right in the Related Product / Service but eMClient version 3.5 is not shown there, so i selected version 3.0