Your comments

I had a look at it, but the new version uses a completely new authentication method. Also, apps using the new SDK were rejected.  See http://forums.dropbox.com/topic.php?id=59350 

At the time I last looked when I finished the update for Textastic 4.1, there was no official release that wouldn't result in a reject, but there was only a beta version. I plan to update it in the future, but it is not that easy.
You can already do that: just enter the name in the address field in the preview browser and hit return. Textastic will use that file for all subsequent previews. 

Do you have the latest version of Textastic installed?
Did you get an error message when you tried to upload the file? What kind of file are you trying to update? Did you try to load the site in Safari? Maybe it's a caching issue.
Can you please send an example file with demonstrates the problem to support@textasticapp.com? I can't reproduce it.
You can download the manual as a PDF file from http://www.textasticapp.com/v4/manual/textastic_manual.pdf  and use iBooks or another PDF reader to read it on your iPad.
The next version will allow you to import pictures from the Photo library.
The next version will support zip and unzip.

You could try to use the "ASP vb.NET" syntax highlighting definition. You can select this definition in the File Properties popover after you opened the file. 

It looks interesting, but judging by the Readme, it probably won't support many real life configurations - i.e. modern authentication methods. Also, the last library change was a year ago.