3 days sounds pretty good but it has asked me to login multiple times a day. I have no idea why the cookie is being deleted. I've few extensions that delete cookies and even though I've whitelisted the domain with them, they might have something to do with this.

However I would prefer not to have recaptcha at all. If you want to protect your users you should be implementing two-factor authentication instead of subjecting them into Google's dragnet. I try to avoid Google's privacy rape as much as I can so it bothers me when I'm being blackmailed to help them just because I want to use a website that has got nothing to do with Google's services.