Ah yes that does sound like a local(ish) problem.
Thing is, there are many routes and many machines between you and WP (same for me), and any one of those misbehaving slightly could cause connection problems. I do see that sort of thing occasionally, with WP and other sites, but it rarely lasts for more than 30 minutes or so.
Sometimes the problems are exclusively caused by my ISP so if yours has a status page or help line, it might be worth checking to see if they're having some problems.
Not that it fixes anything, but at least you know.
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Giraffe: a ruminant with a view.