How often does EMC certification have to be repeated (especially in Australia)?
You generally don't need to do new tests. The test you have done before putting the product on the market are what applies. The age of the test protocol is not relevant, as long as the test complies with current legislation.

If the standards or directives change in the future, you only need to carry out new tests if there are significant changes of the technical requirements. If so, there is usually a grace period of a couple of years, during which you can state compliance either to the old or the new directive.

This only applies to products that are in production (still put on market). You don't have to make new tests for older products that you don't sell any longer, even if they still exist on the market.

Though of course, you will have to carry out new tests if you have made significant changes to the product. Particularly if you changed things that may have impact on EMC and radio. (Most notably changes to voltage regulators, clocks/oscillators or changes to anything radio-related.)



However.

In this specific case, I think your customer might have a valid point - it would appear that these standards are superseded(?). See this, note "Superseded by EN 50561-1:2013 EN 55032:20122". I did some very brief research and it appears that they were updated together with the new European EMC directive 2014/30/EU. 

EN 55022:2010 was listed as expired at 1.12.2013 by the "EU Official Journal" (European law) and it is not part of the current list of harmonized standards for the EMC directive. Apparently you should now follow EN 50561-1:2013 instead, so there might have been significant technical changes.

When it comes to EN standards, the rest of the world that accept such standards typically updates their legislation accordingly whenever EU changes the standards/directives.

Anyway, I only did a brief check and I don't know these standards, so if I were you, I'd go double-check this with some EMC expert at your nearest test house.

If you did tests in 2014, you'd think a professional test house should have told you about these on-going/upcoming changes.