When you say the rhizomes are exposed - I gather you meant they are not covered by soil. Are they at all shaded by other plants? Weeds or ground cover plants can be sufficient to prevent warming of the rhizome.
Tall bearded irises are reasonably greedy feeders, and it is generally a good idea to feed them in autumn when they are making increase, and about 6 weeks before they bloom in Spring. They should not get too much nitrogen, but will benefit from potassium and phosphates, and a good liming in winter, at least 6 weeks before feeding them.
If the roots of your irises do not go very deep, they may not be able to gather enough nutrients to grow well. If you have light soil, you may need to plant them a little deeper, to prevent rocking. This occurs when the wind blows on the fans and moves the whole plant slightly, making the rhizome rock in the soil, and fail to develop a secure root system.
Some cultivars do not make sufficient increase, and growth, to flower every year, particularly if the soil is a little on the poor side. They may take 2 years to store up enough energy in the rhizome.
If you had a very wet season, you may have had rotting off of the flower bud early in the season. The bloom stalk comes from the central (mother) rhizome, and excess wetness or frost at the time that this emerges, may cause it to rot.

They are just a few ideas for you to think about. Let me know if any of these ring a bell with you.
Cheers, Jan

Jan, is the time for iris division just after flowering? I presume before a growth spurt begins?

Thankyou for the information Jan. Perhaps I need to feed them as everything else seems OK. Can I buy potassium and phosphates at a nursery?

Superphosphate is readily available at grain stores, and probably nurseries. Pottassium - can't remember how that comes. Potash I think they sell it as. Garden lime or dolomite are Ok for winter.
Lomatia - I TRY and do mine in early December, but as everyone knows we all go insane preparing for Christmas then. It can take me right through to June to get finished with my lot, and that's only the beardeds. (Most others like to stay where they are)
The early transplants will often flower next year.

Catiekay, Kmart, Bunnings have Pot sulphate in kg bags. Don't get Pot chloride as it pushes up the soil salinity.

Thankyou so much for your help ladies, will try the feeding and see how it goes.

Have I had a sex-change? Wait 'til I go and have a look!!!!