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If you are using Akeeba Backup 3.1.3 or 3.1.4 this is expected, as the ZIP archiver was broken in those versions. Make sure you are using Akeeba Backup 3.1.5.

That said, 7-Zip does not support split ZIP archives. In fact the only archiver utilities which support split ZIP archives are:
1. PKZIP for Windows (naturally, as they are the inventors of the ZIP file format)
2. WinZIP
3. Akeeba eXtract Wizard
4. Akeeba Kickstart

Do note that in the case of split archives you have to download all backup parts. In the Administer Backup Files page they appear as Part 00, Part 01, Part 02, etc. In your output directory they have file extensions of .zip, .z01, .z02, etc. You need all parts in order to extract the archive. If any of those parts is missing you will certainly get the error message you mentioned.

I just tested locally using Akeeba Backup 3.1.5 and Kickstart 3.1.5 on the following configurations: Mac OS X with MAMP Pro (PHP 5.2), Ubuntu Server 10.10 with PHP 5.3 and Windows 7 Home Premium with WAMPserver (PHP 5.2). They all produced split ZIP archives which could be extracted by Kickstart.

I think that you are missing something here. Let me reiterate:
1. Make sure that you download the backup archives using FTP in BINARY transfer mode. If you don't explicitly tell your FTP client to use the BINARY transfer mode, the archive parts will become corrupted during transfer. If you are using FileZilla, click on the Transfer, Transfer Type, Binary menu item before starting downloading the files. Do not download the files through your browser.
2. Make sure that you download ALL of the backup parts! This means .zip, .z01, .z02 etc. If even one of the parts is missing, the extraction will fail.
3. If you are uploading the files to a remote server by FTP, you must use the Binary transfer mode for the same reasons as (1).

I am trying with ZIP and JPA split archives, Kickstart always works just fine. I even tried with my live sites, again the archives produced work perfectly. I am not sure why it doesn't work on your site.

You're welcome!

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