Hi Elizabeth,
Thank you for the great pictures, it always helps to understand the issue.  You don't give a lot of details.  Where is it planted?  In the sun all day?  Or, just morning or just afternoon sun?
Does it receive adequate moisture?  They don't do well when the roots dry out.  Is the soil there sandy?   The mulch you have around it, sawdust, is a good one but it will soak up the nitrogen in the soil before it breaks down.
Nitrogen is one of the major elements that plants need, including rhodies.
It is interesting that what looks to be the green side of the leaf is black and the yellow is only slightly affected.  That could be cold weather.  
However, a fungal disease in the roots may be the cause of the problem.  Phytophthora once in the roots and soil, will eventually kill the plant.  You would need to send a soil sample with plants to a lab to confirm that.
You can cut the stem and look at the interior.  If it is all brown the stem is dead.  Live stems if bent gently will bend without breaking, 
The plant is still trying to grow.  I would remove some of the mulch and add a manure compost, either chicken or steer manure (both high in nitrogen content).  I would also start a liquid fertilizer, fish emulsion, to try to beef up the stamina of the plant.  Cover the manure with the sawdust.
With the liquid fertilizer, follow the directions for strength, too much is really TOO much and will burn the plant.  Make sure the manure is wet and the water is getting to the roots.  Stick your trowel down about 4 inches  and away from the plant by about 15 inches to check the moisture of the soil.  You do not want to cut the roots.
If the placement of the plant is directly in a windy area, that will dry out the plant as well.  For the time being, you could put a chicken wire fence around it and cover the fencing with row cover.  That will dissipate the wind, but allow the sunlight to come through. Use the summer weight row cover.  Again you can purchase it in the store.  It is a spun polyester, white in color.
The rhody behind the one you are concerned with does not look really healthy either.  Same treatment for that one would help.
If it is a root disease (there are several), then this treatment will not help.  However, I believe it is worth trying.  
The acidic level of the soil is also very important for rhododendrons.  They like a very acidic soil in the area of 5.5.  You can buy pH soil test kits in a store.  They are not as accurate as lab results but you will get an almost immediate result.  If your soil is not as acidic as it should be, you can add gypsum which will give the plant calcium as well as sulfur, lower the pH of the immediate area around the plants.
These dry products I have suggested do take time.  The liquid fertilizer should show some immediate results such as greener leaves or more rigidity of the leaves.  Do not remove any of the leaves or other greenery.  They are producing sugar for the plant.
Rhodies do not tolerate afternoon sun well at all.  They need dappled shade or morning sun and shade in the afternoon.
I am adding some reading material for you to peruse:
https://extension.oregonstate.edu/news/spring-care-tips-keep-rhododendrons-azaleas-thriving
This second link is from The Spruce:
https://www.thespruce.com/rhododendron-growing-guide-7109537
Please re-contact us if you have further questions or questions about my response.
 

You are welcome. If you can stabilize the plant with the fertilizers and keep it going for a couple of years, it will probably take on a vigor on it's own.