Posted: 29/06/2016 at 19:05
The best time is in early spring but if your plants are showing signs of stress or starvation I'd do it as soon as they've finished flowering.
The RHS has this to say about re-potting rhodos which are also ercicaceous shrubs:-
Container cultivationJohn Innes ericaceous loam-based compost makes a good compost choice, generally providing easier management of watering and feedingRHS research has found that soil-less potting media including ericaceous peat-based and peat-free potting compostsare suitable for rhododendron growing. However they can lose their structure over time leading to poor drainage and an airless root environment, causing leaves to brown and die back. Re-potting every other year into fresh potting compost in early spring as soon as signs of growth are seen is recommended. In the intervening year, replace the top 5cm (2in) of compost. You can re-pot back into the same pot if you trim off up to a third of the roots to make room for fresh potting compost.
and this is what Wyevale's has to say about azaleas in pots:-
To care for azaleas in pots, choose a wide container and stand it on pot feet to ensure good drainage. Plant azaleas in an ericaceous compost - soil based composts have a better structure than soilless ones, supporting plant growth for much longer and making watering and feeding easier. If you can only find a soilless ericaceous compost, ensure the best care for your azaleas by repotting them every other spring into fresh compost. Give container-grown azaleas a frost-free, shady spot on the patio and water them regularly in summer. To ensure the best care for azaleas, use rainwater if you can, which is less alkaline than water from the tap. Don't worry too much though if supplies run out in a dry summer, a month or two of tap water won't cause too much harm.