A friend of mine is a trained electrician who built a new house with a similar set of smoke detectors. Hard wired with backup batteries, all new from the stock of his employer. He encountered the same issue as you. In the end it turned out that the best before date of the original batteries had passed. So although the batteries still showed a solid 9 V on a multimeter, they didn't work consistently. Fresh batteries did the trick.
Changing the batteries and doing what Pembquist said should help.