Around here I've walked up on deer that I had hit less than an hour before and had half it's rear chewed out by yotes. Thats the bad part of bow hunting around here. Even with a perfect double lung you are risking yote damage. DRT doesn't happen to often with archery equipment.
Whino, from your description I'd have to agree with RR and the others. You have a deer down from a liver shot. I've seen them go for a long way with liver hits and I've seen them go 10 yards and lay down. If it was heading towards the direction of a water source that would be the first place I looked. Gut and marginal liver hit deer will 90% of the time head for water.