The drawing doesn't really tell us much. What are you trying to Snap, and to what, and with what mode(s)? Can you point to the situation(s) you're talking about, and describe what you did at them?
Since Arcs are involved, is it only a matter of view resolution? At lower resolutions and comparatively Zoomed out, curves are broken down into linear segments in display only, but the real curvature is still "known." After you Zoom in and things look like they don't meet, try REGEN to take the lower-resolution kinks out of the Arcs, and see whether they then appear to meet. If they do, use the VIEWRES command, answer Yes to the question, and give it a higher circle zoom percentage number (may as well go all the way to the maximum 20000), to at least greatly reduce the effect.
Kent Cooper, AIA