However if making something more energy efficient causes it to break more often, you have to expand the scope to include the energy costs of manufacturing a replacement copy. Even if the marginal costs of manufacturing an appliance are so low repairs no longer make sense, I still doubt that e.g. more efficient washing machine that you have to replace 3 times over 10 years uses, in total, more energy than one less efficient washing machine that doesn't break for 10 years.
If anything, managing the additional complexity by skimping on the engineering work is what causes the failures--that is, engineering a more complex device with the same or smaller engineering effort.
The ideal situation when engineering a new device is that every part of it is likely to break simultaneously, the day after the warranty runs out. If that happens, you know that your device was made as cheaply as possible, but no cheaper, and that you will never need to repair such a device, because buying a new one will always be cheaper.
Repairs are only an issue when different parts are likely to break at different times.
Isn't it possible that the complexity that makes something energy efficient also causes it break sooner?