Ah, what a bastard! My port was moody-- I had it tested and it had a kink just next to the input. That was after I had it repositioned, but that is another story.
It never worked well for taking bloods but didn't fail during chemo either. Still worth it, from my perspective, but it certainly sounds like yours has gone feral. Totally shithouse, particularly since you had such a hard time making the decision in the first place.
The delay with chemo is also stressful though a couple of days isn't likely to be the end of the world. If you are willing to go commando, have the chemo and sort the port later.