You actually don't want to build a relationship with a particular VC, but rather be part of the VC/angel network in your area. The trouble with spending a lot of effort building a relationship with a particular VC is that there are dozens of reasons why the VC might like you, but be unable to get you money. If you get involved in the VC network, then when a particular person can't fund you, they can point you in the direction of someone that can.
Also, YMMV, but the VC funding process doesn't lend itself to personal relationships being of much use. The thing about VC's is that they usually are not investing their own money, so that they have to justify their investments to a committee and to their investors. At that point, in order to do an investment, they have to have a decide amount of documentation, and once you've prepared the documentation, you can present the project to a number of VC's.