It's been three weeks, and my impatience has had me crack one bottle on days 7, 14, and now 20. There's no carbonation in these bottles, and it doesn't appear to be getting any better over the weeks. I pop the top and if I'm not paying attention, I won't hear the escape of CO2/O2 come out, it's that faint.
At this point, should I continue to let them sit in bottles? After a few more weeks, if they don't carbonate, what are my options? Is it even worth the effort to go through and figure out how to siphon them out and back in?
To add a bit more context to the situation: After I racked it off primary and into secondary for a month, I had just started to wash yeast, and was curious if I could wash the yeast that came off secondary fermentation and bottling. So after taking the beer out of secondary and into bottles, I harvested the yeast in the carboy. Yes, I am no aware that harvesting yeast out of secondary is not nearly as good as harvesting off primary, but at the time I didn't. Before that realization occurred, I had actually pitched one of the yeasts into a batch of beer after giving it a good shot at success with a starter. That harvested yeast did not ferment, and I had to pitch other yeast instead. Not sure how much context that adds as to the health of the yeast in suspension in the bottles, but I figured I'd mention it.
TLDR: The yeast harvested off the beer from secondary fermentation did not ferment another batch of beer made after harvesting, despite using a yeast starter.