The breathalyser a police carries is only an indicator. If you fail the indicator, then you are asked to take another on an evidential breath testing machine. If this one fails or you cannot supply one then they can take a urine or blood sample to test.

There are a number of reasons why a specimen of breath may not have been provided upon request. However, any of these would need to be backed up by substantial evidence:

Medical impairments such as an injury or asthma which would make providing a specimen of breath difficult

Mental health conditions such as extreme anxiety which may impair the ability to provide a specimen on the spot

Police not following the proper procedures when requesting a specimen of breath

It should be noted that the police must, when requesting a specimen of breath, warn you that failing to provide a specimen might lead to prosecution. If they fail to do so then the case may be challenged.