You most likely need to lower the Pixel Detail Block Size. This is found in the Detail settings drawer in the Render dialog. Lower this setting until you no longer see small details dropping out. This may require you to go all the way down to 1.
The renderer starts with large blocks of pixels which are refined smaller and smaller during the rendering process. The refinement continues on every block until the maximum block size is reached. At that point, the Block/volume subdivision limit setting decides which blocks to refine smaller. A setting of four in this field means a four-pixel by four-pixel block.
A block size that is too large may result in missing letters in text, or single-pixel lines in surface textures not displaying correctly. These issues can be especially noticeable in animations.