Interesting. Here's where I experience it:

I'm at a Starbucks, where I've previously authorized Wi-Fi access on my iPad. But you have to log in to the Wi-Fi network by accepting the terms on an iOS system-wide slide-up screen. When I'm writing I usually don't bother, because I don't need to go online for anything.

I don't activate airplane mode because I need Bluetooth to connect my keyboard. So, if I've also left the Wi-Fi functionality turned on and I launch Textastic while at Starbucks, the slide-up authorization screen I described above will come up each time I view the launch screen of Textastic. If I turn off Wi-Fi functionality entirely, the problem goes away.

It's obviously not a big problem to turn it off entirely since I'm not using it, but I grew curious about why it was happening at all. I had a Dropbox account set up in Textastic when I first saw what was happening, so I deleted that, force-quit Textastic and rebooted my iPad, and the problem persisted.

I'm using an iPad 1 running iOS 4.3.3. The next time I'm at Starbucks I'll try to reproduce the issue and confirm that my description above is accurate.

I've used the WebDAV feature in the past, but it's never turned on when I encounter this problem.

Thanks!