I am installing Zenphoto as a subdirectory of a website.

After installation, when I load the homepage, it goes straight to the reinstall.

If I lock the install files, it still searches for the files at loading and I get an object not found error on
Album : zp-core/setup/index.php

Same thing with ZP 1.4.13 and 1.4.12

I get a few warnings during install:
PHP version: 5.3.3
Mysql: 5.1.73
UTF-8 selected
Nothing else and no error message after install.

I am Installing to a /photos subdirectory.
I modified the .htaccess with
RewriteBase /photos

You say you install in the subfolder /photos. Is that also the location you call it? So example.com/photos?

It is common to organize webspace you have several sites with several independent domains on in subfolders.

So if it is installed in /photos but e.g. a domain example.com is linked to that folder then the rewrite base would not be /photos but / since it is the root of the domain. In that case Zenphoto indeed would request re-running setup everytime since it doesn't match. The url in the error you got suggest that case.

The gallery is to be accessed using www.domain.com/photos
The .htaccess and all the files are located in the /photos directory.

But the problem was indeed the rewrite base.
I wrote:
RewriteBase /photos
whereas it should have been
RewriteBase /photos/

Okay, just wanted to be sure. Hm, strange /photos should have worked,at least that's what I use on lots of installs myself, primarily locally. But thanks for the note, I see other CMS also use the 2nd slash so probabl we should change that for compatibility.

Update: Please try the support build, on clean install the rewritebase now gets the trailing slash.