There are spacetimes, most notably the Godel Universe, where time is both a loop and not a loop. Some time directions (from the same spatial point) loop around, others go on forever, never getting close to the point of origin. You can still say, however, that it is compatible with the timeless B-like approach. There is no way to construct this spacetime by taking an A-like fixed spatial slice and evolving it forward in time using the Einstein equations. (There is a loophole, however, where one can lift the Godel universe from flat space using a twisted timelike fiber, but that's a different story.)