It would depend on exactly what the problem was on whether the patch would fix it. It may help to install it, and couldn't hurt. There are also other benefits to patch, such as multiple (2 by default) quick saves.

Check out the Freeze and freeze and more freeze topic. While not exactly the same situation, it is also a case of the game working for awhile, and then not, which a re-install temporarily fixes. Maybe some of the suggestion there will be useful?