It seems that the bug appeared just after updating Thunderbird to v.31.3.0.

Do files with that name actually exist on your hard disk? There should be one per pop mail account, buried down in the Mail folder in the folder for the pop mail account. Do you have them somewhere else?

Matt, thanks for your question. All files of popstate-xx.dat type exist in the hard drive folders of corresponding mail boxes: Thunderbird Portable\Data\profile\Mail\mailbox-name; almost all of them have 0 byte length and are accompanied by popstate-xx.dat.msf files having non-zero length. I noticed that those popstate-xx.dat files which have non-zero length do not have paired popstate-xx.dat.msf files. By now some of the mailboxes have about 200 such file pairs.

I think the folk over at portable apps might have got something wrong in their wrapper.

Just to see if it will work out, delete all of the popstate files with a number and all the corresponding msf files from one of the accounts. Pick one with little in the inbox on the server as if you delete the wrong popstate file a complete downloads of all mail in the server will occur. Note Thunderbird must be closed. They will disappear from the Thunderbird interface, but will new ones be created on each mail check is the next question.

Note that all file deletions must be done with Thunderbird closed.

I closed Thunderbird, then deleted all popstate-xx.dat.msf and popstate-xx.dat files of all mailboxes and launched Thunderbird again. The agent started downloading thousands emails for several years, so I had to stop it and delete all messages from all inboxes of email servers via web interface thereof. Then I deleted downloaded duplicate emails from Thunderbird mailboxes. However this action did not solve the initial problem at all. Thunderbird still continues producing popstate-xx.dat.msf and popstate-xx.dat files. This all seems like Thunderbird Portable v.31.3.0 communicates incorrectly with email servers (note these are different servers but the bug is the same). Is that possible to notify Thunderbird Portable programmers of this issue?

faber_ said

Is that possible to notify Thunderbird Portable programmers of this issue?

Perhaps if you were to post on their support site. Here

To test if bug 239455's checkin is involved, the nightly builds to be tested are... https://archive.mozilla.org/pub/thunderbird/nightly/2013/09/2013-09-05-04-59-33-comm-central/ (should work) and https://archive.mozilla.org/pub/thunderbird/nightly/2013/09/2013-09-11-03-03-41-comm-central/ (should fail). (the other nightly builds adjacent to 2013-09-09 are unfortunately broken)