Why some Helper Engines are Mid-train and others are Pushing at the end?

It probably is a matter of when the helper is needed and for how long. If the helper is on the end he can uncouple after pushing over an incline easily. Just a thought.

Sam posted:

Is there a reason for the placements of Helper engines Mid train vs. at the end?

Yes.

I believe it has to do with slack on the couplers. When engines are in the middle, they can reduce coupler slack when stationed throughout the consist. Also, quizshow had a point. At Horseshoe curve the helpers are on the back so they can be un-attached easily 

This is from a Trains.com post 15 years ago.  Sounds reasonable.

Originally posted by M.W. Hemphill

A mid-train helper (singular) is used on certain trains on certain grades, as opposed to a helper on the rear to avoid buckling the train (pushing it off the track on a sharp curve) from too much buff force. A mid-train location means the helper is splitting its work between both pushing and pulling. Typically they are used only on very steep grades and either very heavy trains, or very long and heavy trains that include both loads and empties. Yes, it takes more work to cut them in and out, but it's not all that big of a deal. The Rio Grande on Tennessee Pass did it very quickly because they did it for almost every train, about 10 minutes to cut in and about 10 minutes to cut out.

A helper can also be applied on the head-end if the resultant force won't exceed the drawbar strength. Rear placement was also limited by the presence of a caboose; Rio Grande was typical for western roads in allowing only eight powered axles behind a caboose; if the rear helper required more powered axles, it was cut in ahead of the caboose.

The Western Maryland Railway was famous for using both in steam and diesel eras. Heavy coal trains and long steep grades dictated massive horsepower to move the tonnage.
Here is a westbound coal train with F-7s and 2 SDs midtrain at the east portal of Big Savage Tunnel in Somerset Co.,PA. back in April 1975. I was 15 years old when I took this pic with a Kodak 127 print camera, 1 year later this trackage was abandoned and now is the GAP trail.