If this tree has been diagnosed with Verticillium Wilt (a common problem with maples), there is nothing you can do cure it. With effective management the tree may live for a few more years, but eventually it will succumb to the disease. It will persist in the soil where the infected plant is, for many years, so do not plant any more maples, or other plants that are not resistant to VW in this area.

Here is some information:
http://www.extension.umn.edu/garden/yard-garden/trees-shrubs/verticillium-wilt/
https://www.extension.purdue.edu/extmedia/bp/bp_6_w.pdf
https://www.rhs.org.uk/advice/profile?PID=255

I do not see any signs of wilt in the third photo you've sent.  Once a branch shows signs of VW it does not "bounce back" to health.  Perhaps the wilt you are seeing on this tree is simply a lack of water.

As far as how the disease spreads, here is a quote from the American Phytopathological Society.  Even though some of the references are to potatoes, the manner of spread is true for all plants:

Spread of the pathogen

The transport of infected planting stock can move the pathogen long distances. In bare root or vegetatively propagated plants such as ornamentals or peppermint, a nursery may spread the fungus by selling non-symptomatic, but infected, planting stock. Similarly, Verticillium can be spread in infected potato seed tubers. Once established in a field or landscape, spread of the pathogen occurs primarily by soil cultivation and movement of soil by wind or water. Verticillium propagules occur in highest concentration in the top 30 cm (12 inches) of the soil profile, but they have been recovered from depths as low as 41 cm (16 inches). Inoculum densities and disease severity tend to increase from year to year when susceptible crops are planted.

I am sorry about your tree.  The best way to ensure the health of the syrup tree is to make sure all of your pruning equipment is sterile, avoid tracking mud, soil 

or debris from the sick tree into the root zone of the healthy one, and water and 

fertilize well.

Thanks for contacting AaE.  Please do so again if you have further questions.