It is very difficult to say what is killing your hemlock, but it does look like it is failing. If you looked closely at the branches and needles, you might see an insect (the wooly adelgid) or it could be a disease of the roots or needles.  Insects can be killed with a systemic insecticide, but diseases will not be cured with a systemic fungicide.  If you want to take photos of the stems and trunks and needles to share, we would be happy to look at them. 

I am going to share some information that was given a client in Pennsylvania - it is not entirely applicable to this situation, since you have dieback and not yellowing, but there is some good information here.  

"Although hemlocks normally shed some of their foliage in the autumn, this doesn’t make the tree die, so as you have determined, there must be something else going on.

Your problem could come from several sources, but it’s not possible to tell for sure from just your photograph. Two possibilities are either Fabrella needle blight or (less likely but still possible) elongate hemlock scale. Here are two links that can help to narrow the culprit down:

http://extension.psu.edu/pests/plant-diseases/all-fact-sheets/hemlock-diseases

http://ento.psu.edu/extension/factsheets/elongate-hemlock-scale

Although these problems need to be eradicated by removing all the infected branches and needles with sterilized clippers, alone, they aren’t usually bad enough to kill a tree without the presence of other stressors. Has your hemlocks’ environment changed in the last few years? They don’t like heavy, poorly drained soil, won’t thrive in very wet or very dry soil, and have a low tolerance for urban stress. They also don’t like winter winds, and their foliage can be damaged by the salt that is used in winter road sprays. If any of those conditions have changed for your trees recently, it could bring about death when added to the stress of needle blight or scale.

If your problem turns out to be Fabrella needle blight, it can be alleviated or perhaps even eradicated by collecting the infected leaves and pruning the affected areas of the tree with sterile pruning shears. Put all the infected pieces in a garbage bag so that they do not spread the blight around your yard. This factsheet from the Pennsylvania Dept. of Conservation and Natural Resources will tell you a bit more about it.

http://www.docs.dcnr.pa.gov/cs/groups/public/documents/document/dcnr_007191.pdf

It sounds as though you’ve taken all the right steps to protect your hemlocks from the wooly adelgid, only to have a different problem raise its head. Once you have determined the source of your hemlocks’ distress, you should be able to give them some additional protection. Good luck!

Anita Finkle-Guerrero Replied September 12, 2017, 11:08 AM EDT

I have submitted your photos to the Plant Disease and Insect Clinic at NCSU.  There is certainly some insect damage (mites, or scale or adelgid?) but whether this is secondary damage to a disease issue I can't tell.  They will email you from the clinic.