Tamed wolves continue to whine even when fed until tail is at fully healed position or when placed in love mode.

Update:

This may be linked to a second problem I had with tamed pets getting stuck in a sitting or standing position. However, I did not report that second issue because I was unable to duplicate it in worlds generated in later beta versions, although the problem persists in the original world.

In that world, taming either a wolf or cat, then exiting and reloading the world, causes the pet to remain stuck in its last position. Because pets stuck in the standing position no longer follow and eventually wander off, the issue seems to be loss of an owner identifier.

If unowned tame wolves whine constantly regardless of health, this would explain the primary issue.