Answer: It may be that the plant is in decline due to old age. Twenty years is a long time for a hydrangea! Other possibilities are root rot (poorly draining soil) or root feeding grubs. The only way to determine whether or not it's a root problem is to dig down around the roots to see what you can find.
You can wait to see what happens next spring before deciding whether or not to remove the plant. In the meantime, if you can get that puny sprig to lay down on the soil, you can propagate the plant by layering. If the sprig is long enough to reach the soil surface, you can wound it slightly on the underside of the branch, lay the wounded area on the earth and cover it with soil. You can anchor it down with a couple of stones. Keep it watered and it should produce roots where it was wounded. When this happens, cut the new plant away from the parent and pot it up. While it won't be quite as large as the original plant for a few years, it will still be a clone of that plant and should grow well for many years to come.
Best wishes with your hydrangea.
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