I am okay with being mentioned once to participate. If I'm able to participate I indicate it. Continuing to ask repeatedly, or nudge to join beyond the first mention only serves to make me decide not to participate and I consider it disrespectful of my time, space, and boundaries.
Don't take what I've said personally. There have been several who have behaved this way towards me and I've had to tell each of them where my boundaries are. When people don't take the time to have some consideration for me, my time, and what I need to attend to in my offline life, it's a real turn off.