Why does google keep de-indexing my inner pages?

This is a brand new, 20 page website with no SEO done on it yet, and after submitting my url's to google, they do index just fine. But after a day or two, half of them get removed from the index and I keep submitting and they keep removing, why does this happen?

The domain isn't brand new but it seems to look spam-free on archive.org, although in recent years it shows the message "Got an HTTP 302 response at crawl time" rather than an actual site. What could be the reason for this constant de-indexing?

The fact that your domain is new. It tends to happen with new sites, that their inner pages are always in and out if index. Don't worry about it too much, it will stabilize eventually.

And if you are not sure about the history of the domain you are using, feel free to send it over and I will check. However if there aren't any manual action messages in your GWT, which I presume you have installed, then it should be fine.

Stop submitting your site to Google. Same thing happened to me several times over the past few years until I finally learnt that fetching and submitting your site via webmaster tools is a waste of time.

The next time you start a new website, build one high quality link to the homepage (that's all you need) and it'll get indexed in less than a week. From then on, Google will crawl and index your internal pages and they'll never drop out of the index once indexed.

Do not resubmit, leave them at it and they will all appear eventually.

Other posters may have missed the obvious. Google tends to not include pages which have content that can be found elsewhere on the internet, or which are thin on content.
If this applies to the pages you are referring to, that would explain it - if you're not offering anything new then your pages won't be indexed.

If, however, you do have a decent amount of unique, well written content then it is just as @Nargil and others have said.

Stop resubmitting. Seriously. Just keep building backlinks and let the site age.

its happen because when your domain is new they not index all pages in starting. so start building backlinks and increase traffic.