An odd one this. Start POLYLINE command. Draw a number of lines and then try to snap to any location on those lines.
No snap possible, even command line entered. ???
Though POLYLINE will snap to other elements.
Also if POLYLINE is left unclosed and 'closed' using Grips the two points do not become one ?
I haven't really noticed this happening before...but who know what these software decide to do sometimes.
Try using the "Close" option under polyline edit - 'pedit'. I have always just done this through the dynamic command pull down menu that floats around with the cross-hairs.