I think the OP was lucky that he wasn't put onto a later flight. In August, my flight out of PER was delayed so that I had a 40 min transfer to my SIN flight instead of the hour. There was also about a 10-15 min taxi and when I asked the ground staff about the gate, I was handed a boarding pass for the next flight.

Turns out the gate was still on Final Call when I'd got through security and was walking past on my way to the Bridge. I could have got angry and complained, but that's just adding stress where I don't need it.