MacBook Pro slow to wake up (new behavior)

I've had a MacBook Pro for about 3 weeks. Two or three times today I had a problem I've never experienced before. After being away from the computer for several hours, I hit a key to wake it up, and nothing happened. I had to keep doing this for a couple of minutes before finally I got the log-in screen. I haven't changed any settings, and I assume that some random, accidental keystroke could not have significantly altered some function. It may not be a coincidence that I've just connected a new external back-up drive, which at the moment is not working correctly and not making Time Machine backups (that's a separate problem I'm still working on). Could connecting this device have affected the start up? If so, what's the solution?