I work in the software business, and there is always someone who wants to escalate. Whether it be a resolution to a software support issue that is unsatisfactory or the fact that a project is not being delivered on time, there is no shortage of people who want to be a squeaky wheel.
Now, don't get me wrong; every customer has the right to escalate an issue. You can build a healthy and long-lasting relationship with your customers if you allow them to escalate and provide an appropriate mechanism to do so.
For me, the process of upward escalation works best. If someone has an issue, you encourage them to escalate first with the person who provided the service. For example, if they had an issue with the resolution to a help desk request, then they should first speak with the person from the help desk who provided the resolution.
If they are still unsatisfied with the resolution, then they can escalate to the next person up the chain of command. This may be the help desk team leader for this example. The escalation should then be allowed to continue up the chain of command as required until it reaches the top of the tree, which may be the CEO.
There is a two-fold impact when the escalation can be resolved in an upward fashion. In my example above, the help desk person who provided the original resolution is the best person to resolve the escalation. If they don't know that there was an issue with the resolution they provided, then how are they able to learn from that and be able to fix it? They are also in the best position to provide an alternate solution that may be satisfactory to the customer. Secondly, this same person is provided with the customer feedback directly, empowered to resolve the issue or escalate it themselves, if they feel it is necessary. This then becomes a great learning opportunity for them.
The opposite to upward escalation is, of course, downward escalation. This is where the escalation starts high up and navigates it's way down the hierarchy until it falls to some poor bunny to resolve. The problem with downward escalation is that it involves far too many people who have no ability to solve the issue. As the escalation cascades down to the person who can fix it, a lot of noise and ill-will is generated. Though the customer may have their issue eventually resolved, you generally end up with a lot of squeaky wheels. The customer then gets conditioned to make noise at the highest level, believing this is the only way to get their voice heard.
So, there is nothing wrong with escalating issues. As long as you start towards the bottom and work you way up the hierarchy, you should find you get a satisfactory solution quicker.