Tested using a large, 64+ rubber tree farm. I noticed the bug after it seemed to take at least 5 minutes for a good amount of sap spots to reappear, which is odd because it would be much faster playing SMP. Also, after leaving the farm outside of render distance and coming back to it I would find most of the sap spots full. Reconnecting to the game would also refresh the sap textures.
I don't know if there is any way to have the textures refresh faster, so perhaps this isn't a bug at all but an engine limitation. At the moment the best workaround is to reconnect to the server.
People were wondering how I was getting so much sap, they thought I was cheating, but in fact I was just reconnecting whenever I went down to my farm.