This mistake is one of the hardest for some clients to get past. Some don't get past it until they get burned by it themselves, while others may never get past it. I'm a big believer in "you get what you pay for" and this turns out to be no truer than when spending on technology.
I've seen it happen way too many times - clients with the best of intentions trying to save money only to end up spending more (and sometimes way more) in the long run. Whether it's for hardware, software, or services cutting corners is NEVER the way to save money in the long run. Almost every time a client tries to take a shortcut, it comes back to bite them. Rather than pay to extend a server warranty (which may turn out to be like $150 / year), a client ends up scrambling to replace the hardware when it fails paying more for the replacement parts, taking longer to get the parts in, and costing them thousands in downtime and lost productivity. Trying to save money by not keeping systems patched and up-to-date results in workstations laced with viruses which end up costing exponentially more to fix. Working with a lower end company because their rates are $10 less an hour but end up spending more time to fix problems results in higher support fees. Reducing service fees by utilizing a "do it yourself" mentality, only delays the pain - and usually turns out to be (significantly) more costly cleaning up what wasn't done right in the first place.
Now don't get me wrong - I’m not saying that everyone should spend without any concern for cost. This would be ludicrous. We all have budgets to work with and to make any business profitable we always need to control costs. However, I am saying that going cheap clearly costs you more in the long run. There's no doubt. We've seen it way too many times for it just to be anecdotal evidence. Again, you get what you pay for. If you go cheap, you will feel the pain.