Do authors need their own domain to use email marketing successfully?

I've run into the issue that my reader magnet through Kit isn't delivering the incentive email to everyone who's tried subscribing. My Kit account is set up with a free Gmail address. Could that be part of the problem? This is something I can't remember ever being discussed. I'm not sure why I'm having so many problems with my reader magnet! Would purchasing an email address with my own domain fix this? Thanks!