There is no sure way to determine a particular publisher's health. That is a sad fact. However you should remember that, unlike what happens with a traditional publisher, a POD publisher is in fact a service provider that you choose to hire, so you are free to shop around until you find a deal you like and a publisher you feel you can trust. There is not an only deal that is available to you where you can either take it or leave it. They may not be 100% effective, and if you do them all you may even find some inconsistences, but here you have a small list of things you can do before you contact a particular publisher:
You should try to look for a site that is clear and informative. A confusing site can be seen as a bad sign. Finding the information you need to make a choice shouldn't be a chore. While it is true that some publishers may have a poorly designed site due to lack of funds, experience, or simply a different taste, a site in which navigation is deliberately convoluted may be used to hide some details that are less than ideal from an author's perspective. You probably shouldn't rule out a publisher because of poor site design, but seeing this as a warning sign may be a good idea.
The site must feature either a copy of the contract or at least a clear description of the spirit of the contract and detailed information about how much you would be expected to pay for what. Most publishers have a copy of their contract on line, while this may be seen as ideal there is nothing wrong with a publisher that does not include this material, as long as all fees and essential characteristics (such as royalties) are clearly outlined.
If a publisher asks for contact information before they will provide you the most basic materials you need to make an informed decision, that should probably be seen as a warning sign, if not an outright reason to walk away. Think of it this way: When you go through a publisher's site you are doing the virtual equivalent of window shopping. If you were walking through a mall and as soon as you approached a particular store an employee were to come out and request all sorts of personal information in order to allow you to take a look, would you comply or would you rather walk away?
All publishers advertise and try to make their packages look as good as possible, however if a site features more misleading advertisement than you feel comfortable with, then that could also be seen as a warning sign. There is a fine line between exaggerating and outright lying, and while I am willing to admit that exaggerating may be seen as a necessary evil in order to be competitive, anything that crosses the line to become a lie is, to me, a very dangerous precedent. If the publisher is willing to lie about this, how can I know that he/she can be trusted? The "misrepresentations" you may find at a publisher's website can be divided into to different categories: misrepresenting themselves or misrepresenting their competitors. Of course, some publishers are rather ambitious and so they'll do both.
Try to see what others have to say about the publisher. Do a thorough on line search, visit the newsgroups and so on. Look for both positive and negative comments. Obviously finding a publisher with a virtually spotless record may be nearly impossible. Read those comments carefully, but try to remember that people usually complain more loudly than they praise. Obviously a recurring concern should be taken seriously, and even an occasional problem can be telling, but this particular method may be misleading. Unless a very serious problem becomes apparent, it probably shouldn't be seen as definitive. You should also take into account when a particular problem was reported. Messages posted to a user group or a mailing list may remain in the archives long after the problems themselves have been solved.
Try to contact the authors of the publisher's latest releases. POD publishers can change very quickly and a publisher that was providing a wonderful service six months ago may have undergone significant changes since then (or it may even have been sold), and then again, one that was doing rather poorly may have been restructured. The authors of the publisher's latest releases may be your most accurate source of current information. Luckily a fair number of POD published authors maintain a website, so you should probably find a link to a site that features the author's e-mail by searching for their names (and maybe their book's title) using a search engine. Ask them about their experiences with the publisher, whether or not they would be willing to release another book using the same company and so on. One aspect that is particularly relevant is to ask them about their experiences concerning customer service once the contract has been signed and the setup fee paid. If a well established publisher has released less than a dozen books within the last six months that should probably be seen as a warning, for a new publisher that may not be as serious.
Check out whether the publisher's books are really available through those channels they promote as options that are open to you. Check whether those books are shipped within a couple of days or whether they are classified as special orders. Is there an additional fee involved? Then that would probably be a bad sign. You should also make sure that their retail prices through external channels are competitive, because some publishers may have their books discounted at their website, and this retail price shouldn't be used as a reference. Keep in mind that while a couple of recent releases may be MIA (distributors don't usually consider fixing mistakes that affect POD published books to be a very high priority), if you find that a significant portion of the books by a specific publisher are missing that could signal a problem.
If you are dealing with a publisher that is based in the US, you may also want to take a look at how many books they have registered before the Library of Congress, and when did those registrations take place. Some publishers may have been very active in the past and survive on former glories for a while. This system may not be entirely fair, since not all books are registered with the Library of Congress, so you may want to complement it by doing a search at a major retailer's site for books that have been released by that publisher within six months. Using the database from the Library of Congress has the theoretical advantage of enabling you to filter out the serious works, but of course this doesn't always work.
When you have narrowed down your options to a reasonable few, you should probably consider the possibility of ordering one or two books from each of those publishers to get a better idea of how their books look and feel. Torture those books. Do they fall apart? How does the paper itself feel?
Then, if you are satisfied by what you've found, you should contact the publisher, but before you sign up try to get a feeling for the person on the other end of the wire and trust you instincts. No matter what, you really shouldn't let anyone rush you into making a choice. Take your time.