Error: Transferred a partial file

Please try to enable the "Debug Log" setting in the connection's settings screen. Tap on the (i) button on the right side of a connection to change its settings. This creates a log file when you try to connect to the server which might help you find out what's wrong.

I had a look at the log file, but I am not that much wiser. There are a few warnings about the certificate being issued for a different domain to where I am connecting (I am connecting via local IP), but I do not see how that can be related.

The actual errors related to the file seems to be the following:
"0000: 550 The system cannot find the file specified. .== info: Given file does not exists."

I can upload files via normal FTP using Textastic, and I can upload files via FTPS using Filezilla from a different computer. I am however seeing some strange behaviour in Filezilla where the file is uploaded and then I get a warning about overwriting the file I just uploaded.

Seems this may be a server issue, and not a Textastic bug. I need to investigate a bit more, but I may have reported a false positive here. Sorry if so :/

It appears this was an issue with TLS 1.2 on Windows FTP servers. Hotfix available here: 
http://support.microsoft.com/kb/2888853

Not sure why Textastic gave a different error message than Filezilla, but the error in Filezilla (550: The supplied message is incomplete. The signature was not verified.) pointed me directly to the microsoft hotfix.

It's great to hear that you could figure out the problem.