When mine acted wonky, I changed the battery and it was cured. Not the same behavior as yours but it might be worth a try.
Thanks for the suggestion, Anne. This is a brand new monitor, so I don't think that is the answer, I'm still stumped. Maybe I need a heart, like the tin man???
But you never know how long the strap was sitting on a shelf somewhere and so the battery could just be old or even defective.
I dunno, the new heart idea is the best so far, I think.