This is a bit geeky, but the signature appearance that you see on the page is not the signature, but just a graphical representation of the actual signature. The actual signature is a blob of hex encoded data in the PDF file that you don't really see. That aside...
When you create a digital signature the first thing Acrobat/Reader will ask you to do is select a digital ID to sign with. Acrobat then reads the digital ID and amasses some information to use to create the signature appearance. It then fills in the form field (a signature field is just a special use form field) with the appearance, BUT the signature still hasn't been created. The next thing Acrobat does is asks you to Save the file to disk. This is more geekiness, but it much safer to compute the signature byte range on disk then it is in memory. The simple explanation is it's harder for the bad guys to manipulate the bytes on disk then it is for them to control the bytes in memory and because a digital signature provides document security we err on the safe side and require the file to be written to disk before the signature is created. The other safety item is, we want to sign the signature appearance so that someone can't come along later and modify the appearance without breaking the signature, so it (the appearance) has to be created before the signature proper is created.
So at this point you've seen the signature appearance and thought that the signature has been created, but it hasn't. When you try to save to the network folder something is preventing Acrobat from saving the file and what ends up happening is the file is rolled back to the pre-signature state and the signature appearance is removed. The file is in essence untouched.
All of that aside (which is probably more than you really wanted to know) the real question is why can't the file be saved to the network folder. This isn't really a digital signature issue, but rather a network permissions issue.