I tried to search for this issue before I posted here but I couldn't locate a solution to it
I have got a gmail account setup on my desktop Thunderbird (IMAP not POP3) and the same account is setup on my Samsung Galaxy S3 LTE.
When I delete an email from my Thunderbird it won't be deleted from my Samsung Galaxy S3 gmail account.
And when I delete an email from my Samsung Galaxy S3 gmail account it won't be deleted from my Thunderbird.
I have got those setting on my mobile
Setting --> Accounts --> Google --> click my gmail account --> Sync Gmail is checked
Apps --> Gmail account --> press Menu button --> Settings --> click my gmail account --> Data Usage --> Sync Gmail is checked and Days of mail to sync set to " One Day ".
I have no problem when I am using the gmail account on my other phone which is iphone 4S,,,, means sync happens smoothly between iphone and Thunderbird