Internet Radio Streams Sputter/Quit...

I'm only about a half degree removed from being a complete beginner in the area of computer audio so forgive me if I'm asking something that's been covered a thousand times here: On both my home internet service (first broadband speed upgrade above basic as per Comcast) and my mobile phone unlimited data plan connection, I tend to lose connection to internet radio stations after they've been playing awhile. This varies quite a bit according to the particular station -- I can't keep my #1 favorite, Blues oriented "Radio 66" apparently originating in Europe, tuned in for more than an hour or two maximum. Generally speaking, if I log onto any internet radio station say, at 9am, it's not going to still be connected by 3pm. Any advice?