When our plant was younger, it was susceptible to mildew but it has become more disease resistant with age.
One of the things I've noticed about this rose is that it tends to set hips very readily and towards the end of of a profuse flowering flush, as it starts to make hips, its disease resistance is at its lowest. If I remove the spent blooms conscientiously, it makes strong new growth and remains in good health. If I don't deadhead, it makes beautiful big hips - lots of them - begins to look a bit poorly and starts dropping leaves.
In our climate, if it defoliates in summer, it is then vulnerable to sun scorch on the stems and needs to be nursed back to health.
Despite this, I'd hate to be without "Not Adam probably Mme Berard". Its blooms are so very beautiful. Exquisitely so. It can take some shade and one of the best plants I've seen is at Ruston's Roses in Renmark, South Australia, where it grows very happily in a dense shrubbery with a cool root run and partial shade that gives some relief from the blazing summer sun.