P510: AF zooms past focus?

I'm sure it's me, but I don't know what I am doing wrong.  Set in P mode with AF and/or Centered,   I am usually within five feet of the subject, in sunlight, zoomed, but it won't focus.  It tries, and I see it zoom past a good focus into blurriness and then flash red - that AF can't get a focus.

Am I zoomed in too much?  (When I have remembered to look, the shutter was 1/250 and aperture is something like 3.8, so it seemed like I wasn't zoomed in too much.)   Popping up the flash doesn't help.   I snap anyway and yes, it is a blurry picture!

jan