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I would strongly suggest sending your neighbors a certified letter stating that, per your earlier conversation, you consider this tree to be a hazard due to its proximity to the power lines.  Then, when and if something bad does happen, you will have a record of having informed them of it and they won't be able to say "we didn't know."

You say the county has told you it is the neighbor's problem.  Did you contact the local electric company?  They should care very much about the situation.

I would also recommend taking lots of pictures showing the proximity of the tree to the wires and that it is obviously dead.

Dead trees do sometimes stay vertical for a very long time, but it sounds like a tense situation for you.  I understand your desire to not inflame the situation, but it doesn't sound like there is anything more you can do that won't have the potential to do so.  So it becomes your responsibility to look after your own interests in the most reasonable way possible.

For my money, never ? I do a walk-around yearly in the summer (when easy to work on and before the heavy fall winds in our area) and look for trees with dead crowns, losing branches everywhere but at the crown, brown branches (evergreens) or leafless branches, leaning trees, trees with visible rot, trees with major bark loss, trees with seriously damaged or eroded away roots, etc. If none of those symptoms, then I call our 100 or so trees good for the year.

Of course, the bigger the trees and the likelihood of house damageor powerline loss (especially in winter) if there is a major branch or tree fall comes into play also. I trim and cut my own trees when needed regardless of size, so my level of confidence in being able to handle anything comes into it.

If you are worried about one or more trees, call an arborist to check them out - then I would say unless there is evidence of damage - ESPECIALLY leaning trees or major branches not leafing like the rest of the tree - I would not worry having them looked at more frequently than every 10 years or so.