Views block settings are lost when using AJAX

Problem/Motivation

Views block displays that have the items_per_page customizable and use AJAX will lose the block instance setting when the view is rendered through AJAX (for example in a pager link).

Steps to reproduce on a clean install:

1) Create a view of nodes with a block display
2) Make sure the "Items per page" is checked in the Block Settings -> Allow settings
3) Under "Advanced", check "Use AJAX"
4) Under Pager -> Use pager, select "Paged, 10 items" to define 10 items per page as default for this view.
5) Save the view
6) Go to /admin/structure/block/list/bartik and place this block somewhere in your page. In the modal block configuration form, set "Items per page" to 5.
7) Generate a bunch of content (say 20 or 50)
8) Visit a page where your view block is visible. You will have the first 5 elements displayed
9) Click the pager link to navigate to the next page.

Expected behavior:
- You will see page 2 of results with the next 5 items.

Actual behavior:
- You see page 2 of results with 10 items.

If you use Ctools (with the submodule ctools_views) then all of the additional settings exposed by the module are affected by the same problem.

Proposed resolution

Remaining tasks

User interface changes

API changes

Data model changes