It's okay for casual speech, but the sentence would sound better with "afford" + infinitive. The use of "being" is grammatically wrong, though. It should really say, "We can’t afford to have our customers BE held up by downtime." Because this is a quote, the mistake is understandable and not very important. People often make small grammar errors in speech.

From my point of view, afford + infinitive and afford + gerund are basically the same and can be used interchangeably. In fact your sentence would be correct even if you used afford + infinitive and would still have the same meaning.