BD Whirlpools
I'm not sure if the models here in Aus are anything to go by, but the timer based ones I saw some time back (and even digital ones now) that are Energy Star models (They have the logo printed on them) seem fairly robust on the front, but are pretty crappy inside.
From the reviews I've seen online for these, transmission failures, timer failures, linting issues and "assorted other" failures. Personally, I've seen one in action: Very slow spin speeds (Very wet clothes at the end of the cycle), agitation sounds like a steam train (Chugga Chugga Chugga with lots of splashing, hissing and wooshing sounds). From this, I can say: AVOID THEM LIKE THE PLAGUE!
If you are in the market for a new machine, get a Speed-Queen TL/FL machine, either will work fine for most people.
Failing that, repair your old Whirlpool. These machines were built for Sears and numerous other appliance manufacturers for a number of years: From the 70s right through to the last few years to quite recently, as far as I'm aware. With so many machines in service, it is unlikely that parts will become NLA for quite some time. Even so, members on here that repair machines/scrap them for a living may be able to cannibalise some machines for yours. And if you are really lucky, parts from newer machines could probably be fitted. You could retrofit newer parts or get others restored as needed.
However, if you are "bent" on getting a machine when your current one dies, ensure you sell it to someone who might fix it, and get yourself a vintage machine or SpeedQueen, as recommended above. This will ensure you have properly clean clothes for quite some time.