Consider starting with that list, and look for recent offers by them. Also read the comments on each offer looking for irregularities. Lowendbox has a decent community, they know when an offer smells, or when a fly-by-nighter drops in. Granted it won't be perfect, but you can reduce the risk of a provider disappearing all of a sudden with a little bit of reading and digging.
Two in particular I find trustworthy: VooServers and Evorack
But beware, many low-end-box type providers use stock standard off-the-shelf tools and software, including WHM. So if you have a religious disagreement with passwords in cleartext emails, you should steer well clear of lowendbox/WHM combinations and go for a highend supplier instead.
Or perhaps a more practical method, don't use a secure password when you sign up, and make it more secure on the VM itself when you log in for the first time
YMMV.
http://www.lowendbox.com/blog/top-providers-2011q1/
http://www.lowendbox.com/blog/top-low-end-vps-providers-2012...
Here's a list of popular low end VPS providers at the LowEndTalk Wiki that is based on the same data used for the above lists:
http://www.lowendtalk.com/wiki/top-providers
Here are the popular low end VPS providers I made note of when I researched this subject recently:
http://buyvm.net/ (limited availability; see http://doesbuyvmhavestock.com/)
http://www.ramhost.us/ (owns http://tinyvz.com/ and http://tinykvm.com/)
In addition to LowEndBox and LowEndTalk, the following two sites had some good info about low end VPSs:
I didn't end up playing with any low end VPSs because none of the providers I evaluated offer users the ability to clone VPSs, which is one of my requirements.