The answer is it depends on a number of factors. Are you doing a Seed round or a Series A or Series B or later financing? Also, are you asking an individual who will write you a check or a firm with a partnership.
Individuals might write you a check after the first meeting if you've already dictated the terms of the deal. I've seen small seed firms do it, but it is rare.
A firm will usually have a partner meeting where they will make a go or no go decision. So, the key item is for the partner who is your champion to get you into their partner meeting for a vote. Obviously, if they invite you to the partner meeting to present, you are in pretty good shape.
It sounds like you are in an ambiguous area. A question you could ask is, "So, what is your process for making an investment decision?" Based on their answer, ask if they are ready to go to the next steps. If they hesitate, you can ask why aren't you going to the next step if that is part of their process.
For example, they might say we'd like to talk to a few customers. You should queue up the meetings. If they don't move pretty quickly, you know there is something else going on.
If they say something ambiguous like, "We'd like to see more traction" with no follow ups, just assume it is a no.