If I'm not convinced to invest after one meeting, I usually don't invest. On the other hand, if I'm convinced after five minutes, I'm usually asking where to send the wire by the end of the meeting.
Armory is a good example of an open source/open core company I did invest in. They had me convinced in just a few minutes. They had an answer for every one of my objections and made me feel like I'd be missing out if I didn't invest. And so far they're doing really well and it's one of my best investments to date.