I have no "Save Image" option after updating to 7.1.

Try a reset: Simultaneously hold down the Home and On buttons until the device shuts down. Ignore the off slider if it appears. Once shut down is complete, if it doesn't restart on it own, turn the device back on using the On button. In some cases it also helps to double click the Home button and close all apps BEFORE doing the reset.

Are you trying to save the image from your google search or from the web page that the image will take you too? Because, I have the same problem and can still save images from the web site but not within my google searches. I think it is actually Google and not Apple that is blocking this.

Depending on what mechanism is used to display the images, the ability to lock down and prevent image download could be an option (or it uses something that isn't fully compatible with Safari for iOS).

I tested this with both Safari and Chrome browsers and had the same issue with both. at google.com I was not able to directly save an image from an image search. But when I went to the website I was able to.I don't know if it is Google or Apple but something changed that prevents the save image option to appear on an image when you long press on it in a google image search.

I just checked Bing.com and when you do an image search there, tap the image to enlarge it, you can long press and save the image directly from Bing.

And I was curious so I tried Yahoo.com and it also lets you do a long press and save image when doing an image search.

I went back to my iPad running iOS 7.0.6 and Chrome will let you save the image during a google search when you tap display image to view the full size image. So there appears to have been a change in iOS 7.1.

I am guessing it is apple or google worrying about getting caugt up in a copyright fight. But that is just my opinion.

I have this same issue after updating my iPhone 5 software to iOS 7.1. I just did a full restore set up as new same issue. It seems doing a image search and trying to save the image or gif from the Google search results has now been disabled. You can only save the gif or image from the website its on. It seems to be a google problem it happens in Google Chrome app also

This is happening to me too. I think it's caused by the "sensitivity" of the copy option Apple has when you hold down on the screen, it pops up everywhere, especially with pictures and it probably conflicts with the Google Images save option in Safari. Try holding your device sideways when searching for images, it works for me, the save option is not blocked. You could also press on the "..." button on the corner of the image box and select "view image" and then hold down on the image, the save option is guaranteed there. I know it's annoying and strange, but it works. It needs to be fixed. Hope I helped!

Is this a specific site and image, or is it occuring on multiple sites?

When you did the restore, was as a new device, or did you use a previous back up?