Why have my emails been blocked from downloading?

Question

The email below was sent to me saying I have been automatically removed from the CCLIST1 list (Calorie Count Monday) as  a result of repeated delivery error reports from my mail system and indicating my email account does not exist and that I may be permanently unable to receive emails on my OS and iOS devices.
This is the second time in three months it has happened. At that time I couldn't find any help on the web or from computer-savy friends regarding how and why it happened or how to rectify the situation. After a week or two my email was permanently blocked and I had to change my email address and contact a couple hundred people and businesses with the new address -- many hours were spent doing this. I could still read my emails and send them on my service provider's website, CenturyLink. This was very helpful as many of the web accounts I had required email address verifications before they would accept account information changes.
My internet/email service provider tried to help by having me redo setting up the Mac Mail account on my iMac. That didn't work. I also went online to Apple to again use the method for resetting the Mail account as well as look for answers.
I received the email below yesterday, so hopefully I have some time to solve the problem before my email is blocked from downloading to my devices.
Any advice and step-by-step directions on rectifying this problem would be very much appreciated.
Sincerely,
Bonnie
"Tues, 21 Jan 2014 00:02:39
You have been automatically removed  from the CCLIST1 list (Calorie Count
Monday) as  a result of  repeated delivery  error reports from  your mail
system. This decision was based  on the list's automatic error monitoring
policy and has  not been reviewed or otherwise confirmed  by a person. If
you receive  this message, then it  means that something is  wrong. While
you  are obviously  able  to  receive mail,  your  mail  system has  been
regularly reporting  that your account  did not  exist, or that  you were
otherwise permanently  unable to receive  mail. Here is  some information
that may assist you  or your local help desk in  determining the cause of
the problem:
- The failing address is [email protected].
- The first error was reported on 2014-01-06.
- Since then, a total of 2 delivery errors have been received.
- The last reported error was: 5.1.0 Probe failed
PLEASE DO  NOT IGNORE  THIS MESSAGE.  While you  can re-subscribe  to the
list,  it is  important  for you  to  report this  problem  to your  mail
administrator so that  it can be solved. This problem  is not specific to
the CCLIST1 list  and may also affect your private  mail. This means that
you may have  lost some private mail  as well. Anyone trying  to write to
you during  the same time frame  might have received the  same errors for
the same reason."

Answer 1

I read a few more discussions on this problem elsewhere on-line with the suggestion that I had a bug on my computer that hijacked my email account to send emails elsewhere (not that I had any clue on how to discover that on my computer).
I followed the suggestion to access my email account on-line and change my password and make it stronger. I did that and was able to get my emails downloaded to my computer and other devices.
I'm pretty sure that my original problem started when I unsubscribed from the Calorie Counter on-line newsletter by pressing a link at the bottom of the email I received from them. A screen came up that said I was unsubscribed and then disappeared in a flash.The experience seemed odd and weird compared to other times when I've unsubscribed from something.
As a test I resubscribed to the newsletter and then unsubscribed. I was directed to one of CCounter's internal web pages and went through a couple of steps in order to finish the process... all very professional and obviously on the newsletter's website.
So the lesson I learned was have a strong password for my email and change it occasionally. And do the same for other accounts that are password protected.