Ignoring problems sounds terrible, but when done consciously is a great thing. There are problems whose prevention is simply not worth it. The mistake that a lot of people make is treating all problems as if they were equally severe and equally likely to occur and that's simply wrong. Is spending money flood-proofing your basement worth it? Depends on how often your basement floods and what you keep in there, right? Similarly, engineering around problems increases cost and complexity and should only be done when is worth it.
Two questions need answers: how often can this happen (frequency) and how bad will it be (impact).
Impact: A problem could range from terrible (we lost the database!) to annoying (user gets an error and has to reload a page) to almost guaranteed to not be noticed (inbox lights up after 3 seconds instead of 1).
Frequency: Some things happen almost never. If something goes wrong in your internal app when a transaction is committed on the first second of a year, chances are this will never actually happen. If you are writing a multi-user app that hiccups when a database changes underneath it - that's going to happen all the time!
The decision to prevent is almost always a function of both factors. Unfortunately a lot of people are bad at naming, much less assessing, them. But since you are now in the know, you can use this handy chart to drive the prevention decision.
|Almost Never||Once in a While||All The Time|
|Terrible||Safeguard against catastrophic, unrecoverable issues regardless of likelyhood. The consequences are simply too terrible.|
|Annoying||If it's realistically not going to happen, and if it does happen once it's not fatal, leave it.||Annoying your users sucks but maybe OK if really infrequent.||Don't expose your users to repeated annoyance! These must be handled.|
|Barely Noticeable||If your users won't notice the issue, and it doesn't happen all the time, it's probably OK.||It's weird that your users won't notice if the system experiences a fault on regular basis. So use your judgement.|