Everyone, of course, experiences the vanishing prospect and, on occasion, the vanishing "buyer."
You'll never eliminate them, but there are things you can do to diminish them.
First, understand that a small portion of them were never prospects to begin with--they were just pumping you for information. This "prospect" can appear for a number of reasons: a competitor shopping you; someone thinking about getting into your business fishing for for information; someone who is unhappy about a purchase trying to "research" other people in the industry to see if he really got taken or if there is some way to they can get the other salesperson or company to make good; have already made up their mind about whom they're buying from and are simply looking for conformation about one or more questions they still have and want a "third party" conformation of what the other salesperson had told them; and any number of other reasons. Often these people are relatively easy to spot--they tend to present themselves as just the average guy off the street who knows nothing about your industry and then asks too many highly specific questions that the typical buyer wouldn't ask.
Secondly, there are people who are very, very early in their purchasing process who are also at this point simply seeking information. They may be thinking about buying a home, a new car or some other product many months in the future and don't want to reveal that for fear you won't be willing to spend the time answering their questions--and they don't want someone haunting them for months. So, they get the information and then simply refuse to acknowledge you again afterwards.
These two groups will be around forever and you'll have your share of them. About the only thing you can do is learn to get good at spotting them--and then make a decision as to whether or not you want to waste time with them (i.e., those in the second group that would be long-term prospects and who you believe will try to avoid you).
The third group are prospects who either decided you weren't the salesperson for them; didn't like some of your responses; got diverted by another salesperson; ligitmately changed their mind about purchasing; or who didn't like your follow-up.
The third group is where you can salvage sales. Some of those folks who decided not to purchase, will change their minds again and may be embarrased to re-contact you because of the time delay involved; some diverted by another salesperson will eventually decide that that salesperson isn't right for them for any number of reasons; and even some who didn't like your responses or didn't feel that you were the right salesperson may come back after interviewing other salespeople.
In order to recapture some of the people you must have installed a follow-up system that 1) maintains open contact with the prospect on a consistent basis (but doesn't overwhelm them with the number of contacts); 2) delivers something of value with every contact (not just a "ready to buy yet" contact); and welcomes them to contact you for any reason--even if just to confirm the purchase they finally decide on is appropriate for them.
You can't eliminate the disappearing act, but if you can spot why they disappeared and continue to court those where you may have a legit opportunity to recapture them, you'll get some sales out it. But if you continue to try to follow-up with those who are just pumping you for information, are shopping their competition, etc., you'll drive yourself crazy. You have to learn to spot who's a real prospect and who isn't.