It’s important to understand that people don't grant appointments based on whether they have the time. (Not the ones worth seeing, anyway.) They allocate their time to people who they believe have the capacity to understand and help with their priorities.
So the question becomes, how can you figure out, in advance, what some of those priorities might be? Their company priorities are likely to be conspicuous at the company website (look on the home page, the press/news release page, and in the annual reports or investor section of the website, if that applies to this prospect). You might find some insights as to the prospect’s professional priorities by snooping around on their LinkedIn profile, or other networking sites. And perhaps their personal priorities might be clear when you look at their Facebook, Twitter, or other social sites. Finally, dig around for some industry news or consumer trends that might be relevant to this prospect… and dig for other research that speaks to challenges they might face or opportunities they may have.
If the prospect matters, it’s worth your time to figure out what matters to the prospect. Find their priorities, and they’ll find the time of day.