Webmail E-mail Block

I've been onto my hosting company numerous times and they keep asking me to contact them when this problem happens again, it's a vicious circle as when it does they ask me to wait for it to "happen again".

Cpanel X comes with my hosting account, obviously the standard webmail programs, which I actually don't use but in this case they serve as a solution. I've set up two e-mail addresses according to my domain name, I receive the e-mail through Mozilla Thunderbird which have all the correct POP3 settings etc etc.

Around 10-20 times a month, all of a sudden I will stop receiving my e-mail, Thunderbird will refuse to download the inbox and sometimes returns a timeout error.

I log into the account via the webmail software "horde" to find all my mails stacked up and that some of them do not have a KB measurement. Please see the below screenshot

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If I "delete" these e-mails without the KB measurement my mail box will then be downloaded by Thunderbird.

I'm completely stumbled as to why this happens. It doesn't seem to be any particular e-mails which arrive like this to the box, sometimes they can be junk but other times business e-mails which have been downloaded perfectly fine before.

I've deleted and setup the e-mail accounts several times from Cpanel. Triple checked all my mail client settings and nothing jumps out at me.