iTunes sometimes doesn't recognize connected device

When I plug in my iPad or iPhone (USB), iTunes frequently recognizes its presence. BUT, nearly as frequently, it doesn't seem to notice the device at all. Un-plugging and re-plugging does no good. The only thing that seems to help is quitting and then re-starting iTunes -- which I seem to need to do more and more often any more.

iPhoto, BTW, seems to always recognize that a new device is present.

Ideas?

Apple has two articles to cover this - one for iTunes on Windows OS and the other for iTunes on Mac OS:

• https://support.apple.com/HT204095#PC - iPhone, iPad, or iPod not recognized in iTunes for Windows PC
• https://support.apple.com/HT204095#Mac - iPhone, iPad, or iPod not recognized in iTunes for Mac

Both start with If your iPhone, iPad or iPod won't connect to iTunes on your PC, try the steps below. Just follow the guide for your OS and consider asking a follow-on question if you get stuck with a specific step. Be sure to list the versions of OS and iTunes in that post as those details will help us help you.