There are many answers and variations to this question. Many bands are strong as a group because of past friendships that members may have had where they have all had a strong inclination to play in a band. Although this leads to an increased chance of arguments since there is none of the formality - if you could call it that - that comes with joining a band through, say, a newspaper ad. Another advantage from the friendship aspect of forming a band is that you tend to have much more fun with your friends, and therefore have a positive outlook on your band. Another disadvantage of starting a band with friends is that while it may sound like a really worthwhile and fun idea at the time, some members do not stay with the band for long, especially if the idea of forming a band came from sitting around with your friends and saying "Oh man, you know what would be cool?" - I'm generalising here, no doubt a lot of hard-working and successful bands started out this way. Also, who's to say that the newspaper ad didn't start out that way as well, but they were one player short?
Another aspect of keeping a band gliding along smoothly is the fact that all of the members are having fun being part of it. Being happy playing regardless of success (or lack thereof). Because if no one enjoys it, what's the point? Bands that are in a slump regarding having fun in the band can shift activities for a while, such as the bassist being the lyricist for a song or two, or adding in a drum solo in that new song you were working on, or maybe switch the backing vocals from the bassist to the guitarist every so often just to keep things from becoming monotonous. It also helps if the band members have the same musical tastes and influences. It could be potentially destructive for a band if one guy likes punk, one likes alternative and the other likes ska but you're all playing metal. (Horrific combination of genres but you get my point).
Another thing that would keep a band going strong, especially as a profession, is your amount of success. Without a decent income, maintaining a band professionally would be impossible. As well as this, most band members would think "Well, we're going nowhere and earning peanuts playing in the bar" and might decide to leave. This is why unless you're going to be able to support yourselves through your band, it should probably be a side-job, however temporary. That doesn't mean that you should play as a band for a shortened length of time because of it. More play-time equals more crowd time which equals a slightly greater chance of a talent scout. But this may not even be the reason why you'd want to play every other weekend in the shopping centre. You may do it purely because you enjoy making music which is how it should be.
A reason why your band may not work out is that as your band gets more well-known, more responsibilities and difficulties come with being a good band. You need to be able to, As Jack Black says, (paraphrasing) "How about having to wake up, at the crack of noon, for your band. Or how about spending HOURS wondering 'What T-shirt should I wear?'". Tenacious D is Comedy Rock though and Black is watering down (holding under a f-cking waterfall) how difficult it is to make the effort to keep your band going, which is also why many band members quit or take a hiatus, because the stress and effort of maintaining their band gets to them. Some people can't handle practising songs, concerts, etc. Nearly 24/7.
So basically (oh, so basically (remember I'm 17)), what helps a band to keep running smoothly is fun, enjoyment, success, pay, ability to make the effort to keep the band running, and to not become bored with how your band works, among other things. But what brings down a band is a potential lack of forethought or planning or the I-don't-really-give-a-flying-continental attitude that a bandmate might have (some may be really reclusive and only show up because it was their idea (I've had first-hand experience with someone in that way) and then decide to drop the whole thing).
Of course, there is much more that affects a band that I have not added. So leave a comment on what you feel helps a band to keep running and enrich the perspectives of potential bandmates everywhere.