The DSL router that I put in as a replacement for the one that failed recently ... failed. I rebooted it, but it connected for two seconds before it failed again, and it did that consistently each time I rebooted it.
So I put in the router that worked for a day or so before failing, and that worked fine, which tells me that it isn't a line fault, it's a router fault.
The router I use is by Cnet, "conexant hasbani", whatever that is. I've been using them for several years. Originally, I had six of them working in parallel, because the best line I could get was 0.5 megabit, but then I was able to get a much faster DSL, so I cut down to three, which left me with three working DSLs in reserve.
I have now used all of those. In my junk box, I see nine non-working routers like this, so they obviously have a limited lifespan. Fortunately, when I originally bought them (several years ago) I bought two spares, and those were still boxed and unused. So I brought one of those into play, and it's working fine.
They only cost me £15 when I bought them, so I'm not really complaining!
I just checked. They are still available! They are now called "Trust" but it's the same box, and they cost £12. But, just in case, I've ordered a "Siemens Wireless G Router 54 Mbps 4-Port 10/100 Gigaset SE587 WLAN dsl" from Ebay, for £4.95 (which is a really silly price, I guess someone got a large number of these as bankrupt stock or suchlike), because maybe it will last longer, and anyway it will mean I have another wireless point in the house.