Bill Carlsen makes a great point.that was the first thing I thought of when I read this post.Often when the blood trail peters out,you are near the end.
When a deer really starts to get in trouble,it may start going downhill if it isn't already.It may not be applicable in your country but they often also head to water.
When I hit the end of a blood trail,I first continue on the same direction I have been traveling.If that doesn't work,I examine some other options.
Another scenario that you have to rule out when you hit the end of a blood trail is that occasionally,an animal doubles back on it's own trail and then after some distance,leaves the trail,headed in some other direction.
I know of several instances where this has happened and it causes great confusion and can send you off on a long,wild goose chase.Back track for some distance and look for tracks going back,changes in blood spatter,blood on the wrong side of the trail or blood drops leaving the trail.
If you are truly at the end of the blood trail,and are starting your grid search,really search,don't just skim.If you are filled with doubt,you may go too fast and cover too much ground,too fast.
Think about how small a surface area a deer's body will cover,in a laying position, and you cannot pass up anything that could hide something close to that size.It could be behind one bush,a log,laying in a depression etc..Check EVERY brushpile,log,bush,clump of weeds etc..
I just know of too many instances where someone missed a deer that he would have found if he took 10 more steps,looked behind a certain tree,checked behind a bush etc..A hunter was here yesterday and told me 3 different stories like that.
It takes a lot of skill and patience to get an arrow in a deer but it takes at least as much sometimes to trail it too recovery and this is where you really have to slow down and apply due diligence.